Atkin-Lehner |
3- 5+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
45045o |
Isogeny class |
Conductor |
45045 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
278528 |
Modular degree for the optimal curve |
Δ |
-7465685748495975 = -1 · 37 · 52 · 72 · 118 · 13 |
Discriminant |
Eigenvalues |
1 3- 5+ 7+ 11+ 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-34965,-4850744] |
[a1,a2,a3,a4,a6] |
Generators |
[1894:1573:8] |
Generators of the group modulo torsion |
j |
-6484907238722641/10240995539775 |
j-invariant |
L |
5.4680861880443 |
L(r)(E,1)/r! |
Ω |
0.16542707099586 |
Real period |
R |
4.1317951734916 |
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 |
15015g1 |
Quadratic twists by: -3 |