Atkin-Lehner |
3+ 5+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
85305a |
Isogeny class |
Conductor |
85305 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1176000 |
Modular degree for the optimal curve |
Δ |
-1244519072489446875 = -1 · 314 · 55 · 116 · 47 |
Discriminant |
Eigenvalues |
0 3+ 5+ -2 11- -1 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-699541,-231274539] |
[a1,a2,a3,a4,a6] |
j |
-21370158463320064/702498571875 |
j-invariant |
L |
0.32952389915658 |
L(r)(E,1)/r! |
Ω |
0.082380971674737 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
705a1 |
Quadratic twists by: -11 |