Cremona's table of elliptic curves

Curve 288a2

288 = 25 · 32



Data for elliptic curve 288a2

Field Data Notes
Atkin-Lehner 2+ 3+ Signs for the Atkin-Lehner involutions
Class 288a Isogeny class
Conductor 288 Conductor
∏ cp 8 Product of Tamagawa factors cp
Δ 110592 = 212 · 33 Discriminant
Eigenvalues 2+ 3+ -4  0  0 -6 -8  0 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-12,0] [a1,a2,a3,a4,a6]
Generators [-2:4:1] Generators of the group modulo torsion
j 1728 j-invariant
L 1.4121235928356 L(r)(E,1)/r!
Ω 2.8175842073531 Real period
R 0.25059119602359 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 288a2 576f1 288e2 7200ba2 Quadratic twists by: -4 8 -3 5


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