Atkin-Lehner |
2+ 3+ 17+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
72624a |
Isogeny class |
Conductor |
72624 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
31373568 = 28 · 34 · 17 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 2 4 -2 6 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-492,-4032] |
[a1,a2,a3,a4,a6] |
Generators |
[38856:319725:512] |
Generators of the group modulo torsion |
j |
51553893328/122553 |
j-invariant |
L |
7.6448210823009 |
L(r)(E,1)/r! |
Ω |
1.013670439334 |
Real period |
R |
7.5417224239525 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993166 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36312b1 |
Quadratic twists by: -4 |