Cremona's table of elliptic curves

Curve 69776r1

69776 = 24 · 72 · 89



Data for elliptic curve 69776r1

Field Data Notes
Atkin-Lehner 2- 7- 89+ Signs for the Atkin-Lehner involutions
Class 69776r Isogeny class
Conductor 69776 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 258048 Modular degree for the optimal curve
Δ 702680875925504 = 226 · 76 · 89 Discriminant
Eigenvalues 2-  2 -2 7-  0  4 -2 -2 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-34904,2173424] [a1,a2,a3,a4,a6]
Generators [-27099:1347794:729] Generators of the group modulo torsion
j 9759185353/1458176 j-invariant
L 7.6284611921458 L(r)(E,1)/r!
Ω 0.48764689961952 Real period
R 7.8217058265296 Regulator
r 1 Rank of the group of rational points
S 1.0000000000078 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 8722i1 1424e1 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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