Cremona's table of elliptic curves

Curve 68265g1

68265 = 32 · 5 · 37 · 41



Data for elliptic curve 68265g1

Field Data Notes
Atkin-Lehner 3- 5+ 37- 41+ Signs for the Atkin-Lehner involutions
Class 68265g Isogeny class
Conductor 68265 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 258048 Modular degree for the optimal curve
Δ 2040372585 = 38 · 5 · 37 · 412 Discriminant
Eigenvalues  1 3- 5+  0 -4 -2 -2  4 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-524790,-146196545] [a1,a2,a3,a4,a6]
Generators [46832081912857626:-2091423715179949837:21122996216707] Generators of the group modulo torsion
j 21925691636751231841/2798865 j-invariant
L 5.0253237820912 L(r)(E,1)/r!
Ω 0.17737937820867 Real period
R 28.330935826795 Regulator
r 1 Rank of the group of rational points
S 1.0000000002118 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 22755e1 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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