Cremona's table of elliptic curves

Curve 57408cx1

57408 = 26 · 3 · 13 · 23



Data for elliptic curve 57408cx1

Field Data Notes
Atkin-Lehner 2- 3- 13+ 23+ Signs for the Atkin-Lehner involutions
Class 57408cx Isogeny class
Conductor 57408 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 49152 Modular degree for the optimal curve
Δ -20633812992 = -1 · 216 · 34 · 132 · 23 Discriminant
Eigenvalues 2- 3-  2 -2  0 13+ -6  8 Hecke eigenvalues for primes up to 20
Equation [0,1,0,-1217,17343] [a1,a2,a3,a4,a6]
Generators [7:96:1] Generators of the group modulo torsion
j -3044193988/314847 j-invariant
L 8.3453937220995 L(r)(E,1)/r!
Ω 1.1828439596389 Real period
R 0.88192039764349 Regulator
r 1 Rank of the group of rational points
S 1.0000000000263 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 57408o1 14352e1 Quadratic twists by: -4 8


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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