Cremona's table of elliptic curves

Curve 57096j1

57096 = 23 · 32 · 13 · 61



Data for elliptic curve 57096j1

Field Data Notes
Atkin-Lehner 2- 3+ 13+ 61- Signs for the Atkin-Lehner involutions
Class 57096j Isogeny class
Conductor 57096 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 31232 Modular degree for the optimal curve
Δ -96337852416 = -1 · 211 · 33 · 134 · 61 Discriminant
Eigenvalues 2- 3+  1  0  2 13+  3  2 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-1707,30982] [a1,a2,a3,a4,a6]
Generators [178:507:8] Generators of the group modulo torsion
j -9947880486/1742221 j-invariant
L 7.1963549999231 L(r)(E,1)/r!
Ω 1.0266480194396 Real period
R 1.7523910005432 Regulator
r 1 Rank of the group of rational points
S 0.9999999999941 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 114192a1 57096a1 Quadratic twists by: -4 -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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