Atkin-Lehner |
2+ 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
72864d |
Isogeny class |
Conductor |
72864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24320 |
Modular degree for the optimal curve |
Δ |
-3497472 = -1 · 29 · 33 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 4 3 11+ -5 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3,-90] |
[a1,a2,a3,a4,a6] |
j |
-216/253 |
j-invariant |
L |
4.5188876498594 |
L(r)(E,1)/r! |
Ω |
1.1297219187065 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72864e1 72864u1 |
Quadratic twists by: -4 -3 |