Atkin-Lehner |
5- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
97175o |
Isogeny class |
Conductor |
97175 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
177408 |
Modular degree for the optimal curve |
Δ |
30487935697375 = 53 · 139 · 23 |
Discriminant |
Eigenvalues |
1 -1 5- -1 -6 13+ 1 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9805,-266950] |
[a1,a2,a3,a4,a6] |
Generators |
[-610:1995:8] [-34:186:1] |
Generators of the group modulo torsion |
j |
172808693/50531 |
j-invariant |
L |
9.6325540553443 |
L(r)(E,1)/r! |
Ω |
0.49052518624342 |
Real period |
R |
4.9093065581296 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000347 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97175u1 7475h1 |
Quadratic twists by: 5 13 |