Atkin-Lehner |
2+ 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
30576a |
Isogeny class |
Conductor |
30576 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-318958897001472 = -1 · 210 · 310 · 74 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 3 13+ -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-95272,11383072] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:3402:1] |
Generators of the group modulo torsion |
j |
-38898423529252/129730653 |
j-invariant |
L |
5.6979813225615 |
L(r)(E,1)/r! |
Ω |
0.54541387858858 |
Real period |
R |
0.87058983190689 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15288i1 122304gs1 91728n1 30576bc1 |
Quadratic twists by: -4 8 -3 -7 |