Cremona's table of elliptic curves

Curve 42966w1

42966 = 2 · 32 · 7 · 11 · 31



Data for elliptic curve 42966w1

Field Data Notes
Atkin-Lehner 2- 3+ 7+ 11- 31+ Signs for the Atkin-Lehner involutions
Class 42966w Isogeny class
Conductor 42966 Conductor
∏ cp 672 Product of Tamagawa factors cp
deg 3096576 Modular degree for the optimal curve
Δ 3.311530003464E+20 Discriminant
Eigenvalues 2- 3+ -4 7+ 11-  4  2 -4 Hecke eigenvalues for primes up to 20
Equation [1,-1,1,-4607822,3706185565] [a1,a2,a3,a4,a6]
Generators [-487:76627:1] Generators of the group modulo torsion
j 549691995827921808987/16824315416674304 j-invariant
L 6.5346410270397 L(r)(E,1)/r!
Ω 0.17040501070228 Real period
R 0.22826014692724 Regulator
r 1 Rank of the group of rational points
S 0.9999999999989 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 42966b1 Quadratic twists by: -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
Back to Tables and computations