Cremona's table of elliptic curves

Curve 52111b1

52111 = 31 · 412



Data for elliptic curve 52111b1

Field Data Notes
Atkin-Lehner 31+ 41+ Signs for the Atkin-Lehner involutions
Class 52111b Isogeny class
Conductor 52111 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 19200 Modular degree for the optimal curve
Δ 66233081 = 312 · 413 Discriminant
Eigenvalues  1 -2  2 -2 -2  0  4  6 Hecke eigenvalues for primes up to 20
Equation [1,0,1,-835,9201] [a1,a2,a3,a4,a6]
Generators [86:263:8] Generators of the group modulo torsion
j 932574833/961 j-invariant
L 4.4993664143561 L(r)(E,1)/r!
Ω 1.9488802636683 Real period
R 2.3086930983864 Regulator
r 1 Rank of the group of rational points
S 1.0000000000097 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 52111a1 Quadratic twists by: 41


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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