Atkin-Lehner |
2- 3- 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
30690bk |
Isogeny class |
Conductor |
30690 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-203035065750 = -1 · 2 · 39 · 53 · 113 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5- -1 11+ -1 3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-27257,-1725361] |
[a1,a2,a3,a4,a6] |
Generators |
[1566:4343:8] |
Generators of the group modulo torsion |
j |
-3071958955278409/278511750 |
j-invariant |
L |
9.0589330893286 |
L(r)(E,1)/r! |
Ω |
0.18577998691279 |
Real period |
R |
4.0634683171323 |
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 |
10230o1 |
Quadratic twists by: -3 |