Cremona's table of elliptic curves

Curve 78400gx1

78400 = 26 · 52 · 72



Data for elliptic curve 78400gx1

Field Data Notes
Atkin-Lehner 2- 5+ 7- Signs for the Atkin-Lehner involutions
Class 78400gx Isogeny class
Conductor 78400 Conductor
∏ cp 16 Product of Tamagawa factors cp
deg 110592 Modular degree for the optimal curve
Δ 9411920000000 = 210 · 57 · 76 Discriminant
Eigenvalues 2-  0 5+ 7-  4  2  2 -4 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-9800,343000] [a1,a2,a3,a4,a6]
Generators [-110:300:1] Generators of the group modulo torsion
j 55296/5 j-invariant
L 6.8586656162156 L(r)(E,1)/r!
Ω 0.70968490251491 Real period
R 2.4160953649994 Regulator
r 1 Rank of the group of rational points
S 1.0000000002785 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 78400w1 19600i1 15680dk1 1600p1 Quadratic twists by: -4 8 5 -7


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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