Atkin-Lehner |
2- 3+ 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
72864u |
Isogeny class |
Conductor |
72864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
72960 |
Modular degree for the optimal curve |
Δ |
-2549657088 = -1 · 29 · 39 · 11 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -4 3 11- -5 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27,2430] |
[a1,a2,a3,a4,a6] |
Generators |
[9:-54:1] |
Generators of the group modulo torsion |
j |
-216/253 |
j-invariant |
L |
3.6950614257659 |
L(r)(E,1)/r! |
Ω |
1.1648601759366 |
Real period |
R |
0.79302681582282 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002594 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72864r1 72864d1 |
Quadratic twists by: -4 -3 |