Atkin-Lehner |
3+ 5- 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
45045j |
Isogeny class |
Conductor |
45045 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-81839095947984375 = -1 · 39 · 56 · 7 · 113 · 134 |
Discriminant |
Eigenvalues |
1 3+ 5- 7+ 11- 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-184884,-33505237] |
[a1,a2,a3,a4,a6] |
Generators |
[1178:36591:1] |
Generators of the group modulo torsion |
j |
-35508450959787987/4157856828125 |
j-invariant |
L |
6.3863913739426 |
L(r)(E,1)/r! |
Ω |
0.11436608903537 |
Real period |
R |
3.1023140142899 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
45045b1 |
Quadratic twists by: -3 |