Atkin-Lehner |
2- 3- 5- 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12090bk |
Isogeny class |
Conductor |
12090 |
Conductor |
∏ cp |
756 |
Product of Tamagawa factors cp |
deg |
72576 |
Modular degree for the optimal curve |
Δ |
3610054656000000 = 218 · 37 · 56 · 13 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5- -2 -2 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-39695,-957063] |
[a1,a2,a3,a4,a6] |
Generators |
[454:-8867:1] |
Generators of the group modulo torsion |
j |
6917223603906560881/3610054656000000 |
j-invariant |
L |
8.2713482714911 |
L(r)(E,1)/r! |
Ω |
0.35826742607195 |
Real period |
R |
0.12215385570503 |
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 |
96720cn1 36270u1 60450c1 |
Quadratic twists by: -4 -3 5 |