Atkin-Lehner |
2+ 3- 5+ 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
30690f |
Isogeny class |
Conductor |
30690 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1408000 |
Modular degree for the optimal curve |
Δ |
2177362811289600000 = 220 · 311 · 55 · 112 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11+ -6 -8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4380075,-3526530939] |
[a1,a2,a3,a4,a6] |
Generators |
[137919534:-9593810967:24389] |
Generators of the group modulo torsion |
j |
12747965531857798561201/2986780262400000 |
j-invariant |
L |
2.2967913455386 |
L(r)(E,1)/r! |
Ω |
0.10436028810138 |
Real period |
R |
11.004144331738 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10230bg1 |
Quadratic twists by: -3 |