Cremona's table of elliptic curves

Curve 50778ca1

50778 = 2 · 32 · 7 · 13 · 31



Data for elliptic curve 50778ca1

Field Data Notes
Atkin-Lehner 2- 3- 7- 13- 31- Signs for the Atkin-Lehner involutions
Class 50778ca Isogeny class
Conductor 50778 Conductor
∏ cp 640 Product of Tamagawa factors cp
deg 696320 Modular degree for the optimal curve
Δ 4206743743168512 = 216 · 36 · 75 · 132 · 31 Discriminant
Eigenvalues 2- 3- -4 7- -4 13- -6 -4 Hecke eigenvalues for primes up to 20
Equation [1,-1,1,-87707,9520075] [a1,a2,a3,a4,a6]
Generators [763:-20038:1] [-277:3674:1] Generators of the group modulo torsion
j 102351523274517609/5770567548928 j-invariant
L 11.385038795138 L(r)(E,1)/r!
Ω 0.43155758785516 Real period
R 0.16488295993884 Regulator
r 2 Rank of the group of rational points
S 0.99999999999988 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 5642g1 Quadratic twists by: -3


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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