Atkin-Lehner |
3+ 5+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
117975q |
Isogeny class |
Conductor |
117975 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
983040 |
Modular degree for the optimal curve |
Δ |
-25970613689109375 = -1 · 38 · 56 · 117 · 13 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 0 11- 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-72663,-10844844] |
[a1,a2,a3,a4,a6] |
Generators |
[372489850:12576435506:300763] |
Generators of the group modulo torsion |
j |
-1532808577/938223 |
j-invariant |
L |
3.3527666923314 |
L(r)(E,1)/r! |
Ω |
0.14145019722983 |
Real period |
R |
11.851403231786 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000128725 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4719j1 10725a1 |
Quadratic twists by: 5 -11 |