Cremona's table of elliptic curves

Curve 69936ba1

69936 = 24 · 3 · 31 · 47



Data for elliptic curve 69936ba1

Field Data Notes
Atkin-Lehner 2- 3- 31- 47+ Signs for the Atkin-Lehner involutions
Class 69936ba Isogeny class
Conductor 69936 Conductor
∏ cp 28 Product of Tamagawa factors cp
deg 72576 Modular degree for the optimal curve
Δ 25287738624 = 28 · 37 · 312 · 47 Discriminant
Eigenvalues 2- 3- -3 -3 -3  0  6 -8 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-757,2159] [a1,a2,a3,a4,a6]
Generators [-25:78:1] [-22:93:1] Generators of the group modulo torsion
j 187648442368/98780229 j-invariant
L 9.4693274890099 L(r)(E,1)/r!
Ω 1.0472277579374 Real period
R 0.32293860137186 Regulator
r 2 Rank of the group of rational points
S 0.9999999999957 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 17484a1 Quadratic twists by: -4


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

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