Atkin-Lehner |
3- 5+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
85305r |
Isogeny class |
Conductor |
85305 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
969408 |
Modular degree for the optimal curve |
Δ |
-918072292462875 = -1 · 36 · 53 · 118 · 47 |
Discriminant |
Eigenvalues |
0 3- 5+ -4 11- -1 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-1297281,568290575] |
[a1,a2,a3,a4,a6] |
Generators |
[417:10000:1] |
Generators of the group modulo torsion |
j |
-1126379500601344/4282875 |
j-invariant |
L |
4.5154297654633 |
L(r)(E,1)/r! |
Ω |
0.43650203774648 |
Real period |
R |
5.1722894485277 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999939527 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
85305q1 |
Quadratic twists by: -11 |