Atkin-Lehner |
2- 3+ 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
31152u |
Isogeny class |
Conductor |
31152 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-36748394496 = -1 · 221 · 33 · 11 · 59 |
Discriminant |
Eigenvalues |
2- 3+ -3 -2 11- -4 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-192,-9216] |
[a1,a2,a3,a4,a6] |
Generators |
[32:128:1] [50:322:1] |
Generators of the group modulo torsion |
j |
-192100033/8971776 |
j-invariant |
L |
5.8064319026311 |
L(r)(E,1)/r! |
Ω |
0.50653378753981 |
Real period |
R |
2.8657673216789 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3894o1 124608db1 93456be1 |
Quadratic twists by: -4 8 -3 |