Atkin-Lehner |
3+ 5+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117975f |
Isogeny class |
Conductor |
117975 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
760320 |
Modular degree for the optimal curve |
Δ |
-15283118343796875 = -1 · 33 · 56 · 118 · 132 |
Discriminant |
Eigenvalues |
0 3+ 5+ 1 11- 13+ -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-221833,40726443] |
[a1,a2,a3,a4,a6] |
Generators |
[-2982:67635:8] [-343:8737:1] |
Generators of the group modulo torsion |
j |
-360448000/4563 |
j-invariant |
L |
8.5159937274775 |
L(r)(E,1)/r! |
Ω |
0.39486051734213 |
Real period |
R |
1.7972577987496 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999964067 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4719l1 117975m1 |
Quadratic twists by: 5 -11 |