Max Order of an Isogeny Class of Rational Elliptic Curves is 8?For which composite $N$ does $X_0(N)$ possess a non-cuspidal rational point?About isogeny theorem for elliptic curvesElliptic Curves over Global Function FieldsElliptic curves with arbitrarily large conductorMust the $j$-invariant of an elliptic curve with an isogeny be integral?$j$-invariants of elliptic curves over finite fieldstwists of elliptic curves over finite fieldsDeuring's result on elliptic curves. Any proof reference
Max Order of an Isogeny Class of Rational Elliptic Curves is 8?
For which composite $N$ does $X_0(N)$ possess a non-cuspidal rational point?About isogeny theorem for elliptic curvesElliptic Curves over Global Function FieldsElliptic curves with arbitrarily large conductorMust the $j$-invariant of an elliptic curve with an isogeny be integral?$j$-invariants of elliptic curves over finite fieldstwists of elliptic curves over finite fieldsDeuring's result on elliptic curves. Any proof reference
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I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been proven? And if so, what is a reference to the proof of the result.
reference-request elliptic-curves
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
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add a comment |
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I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been proven? And if so, what is a reference to the proof of the result.
reference-request elliptic-curves
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
$endgroup$
add a comment |
$begingroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been proven? And if so, what is a reference to the proof of the result.
reference-request elliptic-curves
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
$endgroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been proven? And if so, what is a reference to the proof of the result.
reference-request elliptic-curves
reference-request elliptic-curves
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
asked 10 hours ago
ABarriosABarrios
1087 bronze badges
1087 bronze badges
add a comment |
add a comment |
1 Answer
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M. Kenku, On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $Q$-isomorphism classes of elliptic curves in each $Q$-isogeny class.
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
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Thank you, Carlo!
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– ABarrios
10 hours ago
add a comment |
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1 Answer
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$begingroup$
M. Kenku, On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $Q$-isomorphism classes of elliptic curves in each $Q$-isogeny class.
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
$endgroup$
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
add a comment |
$begingroup$
M. Kenku, On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $Q$-isomorphism classes of elliptic curves in each $Q$-isogeny class.
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
$endgroup$
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
add a comment |
$begingroup$
M. Kenku, On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $Q$-isomorphism classes of elliptic curves in each $Q$-isogeny class.
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
$endgroup$
M. Kenku, On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $Q$-isomorphism classes of elliptic curves in each $Q$-isogeny class.
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
answered 10 hours ago
Carlo BeenakkerCarlo Beenakker
86k9 gold badges204 silver badges309 bronze badges
86k9 gold badges204 silver badges309 bronze badges
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
add a comment |
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
10 hours ago
add a comment |
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