Cremona's table of elliptic curves

Curve 68160cg1

68160 = 26 · 3 · 5 · 71



Data for elliptic curve 68160cg1

Field Data Notes
Atkin-Lehner 2- 3+ 5- 71+ Signs for the Atkin-Lehner involutions
Class 68160cg Isogeny class
Conductor 68160 Conductor
∏ cp 64 Product of Tamagawa factors cp
deg 884736 Modular degree for the optimal curve
Δ -3757206513600000000 = -1 · 212 · 38 · 58 · 713 Discriminant
Eigenvalues 2- 3+ 5-  0  2  4 -2  4 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,342215,-52648775] [a1,a2,a3,a4,a6]
Generators [395:12000:1] Generators of the group modulo torsion
j 1082080622856497984/917286746484375 j-invariant
L 6.5846547193896 L(r)(E,1)/r!
Ω 0.13727915760405 Real period
R 2.9978397823836 Regulator
r 1 Rank of the group of rational points
S 1.0000000000105 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 68160dj1 34080m1 Quadratic twists by: -4 8


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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