Atkin-Lehner |
2- 3- 5+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
61710cn |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
969408 |
Modular degree for the optimal curve |
Δ |
-433947379158260550 = -1 · 2 · 39 · 52 · 1110 · 17 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 11- -2 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-234561,-54023265] |
[a1,a2,a3,a4,a6] |
Generators |
[5214:64353:8] |
Generators of the group modulo torsion |
j |
-55025549689/16730550 |
j-invariant |
L |
10.065283435385 |
L(r)(E,1)/r! |
Ω |
0.10680139551649 |
Real period |
R |
5.2357219713278 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000049 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61710z1 |
Quadratic twists by: -11 |