Cremona's table of elliptic curves

Curve 69776b1

69776 = 24 · 72 · 89



Data for elliptic curve 69776b1

Field Data Notes
Atkin-Lehner 2+ 7- 89+ Signs for the Atkin-Lehner involutions
Class 69776b Isogeny class
Conductor 69776 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 98304 Modular degree for the optimal curve
Δ -525380903936 = -1 · 210 · 78 · 89 Discriminant
Eigenvalues 2+ -1 -3 7- -2  0  3  3 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-10992,448624] [a1,a2,a3,a4,a6]
Generators [-2:686:1] [54:-98:1] Generators of the group modulo torsion
j -1219284868/4361 j-invariant
L 7.0548342657959 L(r)(E,1)/r!
Ω 0.93063820287117 Real period
R 0.94758014499713 Regulator
r 2 Rank of the group of rational points
S 1.000000000009 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 34888d1 9968b1 Quadratic twists by: -4 -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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