Cremona's table of elliptic curves

Curve 7872q1

7872 = 26 · 3 · 41



Data for elliptic curve 7872q1

Field Data Notes
Atkin-Lehner 2+ 3- 41- Signs for the Atkin-Lehner involutions
Class 7872q Isogeny class
Conductor 7872 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 8448 Modular degree for the optimal curve
Δ -66035122176 = -1 · 229 · 3 · 41 Discriminant
Eigenvalues 2+ 3- -3 -2 -2 -1  5  1 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-2657,-55041] [a1,a2,a3,a4,a6]
Generators [915:27648:1] Generators of the group modulo torsion
j -7916293657/251904 j-invariant
L 3.8041388813473 L(r)(E,1)/r!
Ω 0.33185249257101 Real period
R 2.8658356999784 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 7872ba1 246g1 23616l1 Quadratic twists by: -4 8 -3


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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