Cremona's table of elliptic curves

Curve 54288s1

54288 = 24 · 32 · 13 · 29



Data for elliptic curve 54288s1

Field Data Notes
Atkin-Lehner 2+ 3- 13- 29- Signs for the Atkin-Lehner involutions
Class 54288s Isogeny class
Conductor 54288 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 12288 Modular degree for the optimal curve
Δ 57165264 = 24 · 36 · 132 · 29 Discriminant
Eigenvalues 2+ 3- -2 -4 -2 13- -2 -2 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-126,-405] [a1,a2,a3,a4,a6]
Generators [-5:10:1] [27:126:1] Generators of the group modulo torsion
j 18966528/4901 j-invariant
L 7.7355111722773 L(r)(E,1)/r!
Ω 1.4522127617323 Real period
R 5.3267065103134 Regulator
r 2 Rank of the group of rational points
S 0.99999999999973 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 27144s1 6032a1 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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