Atkin-Lehner |
2- 3+ 5- 11- 29- |
Signs for the Atkin-Lehner involutions |
Class |
9570w |
Isogeny class |
Conductor |
9570 |
Conductor |
∏ cp |
357 |
Product of Tamagawa factors cp |
deg |
45696 |
Modular degree for the optimal curve |
Δ |
-1185761280000000 = -1 · 217 · 3 · 57 · 113 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 11- -2 -1 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3625,1657367] |
[a1,a2,a3,a4,a6] |
Generators |
[187:-2844:1] |
Generators of the group modulo torsion |
j |
-5268114828522001/1185761280000000 |
j-invariant |
L |
5.6283952163638 |
L(r)(E,1)/r! |
Ω |
0.39695664007778 |
Real period |
R |
0.039716712958629 |
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 |
76560cg1 28710g1 47850bn1 105270k1 |
Quadratic twists by: -4 -3 5 -11 |