Atkin-Lehner |
3+ 5- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8415g |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
43200 |
Modular degree for the optimal curve |
Δ |
10387972353515625 = 39 · 510 · 11 · 173 |
Discriminant |
Eigenvalues |
1 3+ 5- 0 11+ -4 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-58524,-2362357] |
[a1,a2,a3,a4,a6] |
Generators |
[-118:1759:1] |
Generators of the group modulo torsion |
j |
1126259840967507/527763671875 |
j-invariant |
L |
5.2377886267849 |
L(r)(E,1)/r! |
Ω |
0.32122341183087 |
Real period |
R |
1.0870499957089 |
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 |
8415d1 42075c1 92565n1 |
Quadratic twists by: -3 5 -11 |