Atkin-Lehner |
2- 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312cf |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
-19180575337218048 = -1 · 220 · 311 · 133 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -2 1 -3 13- -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,52671,-4787487] |
[a1,a2,a3,a4,a6] |
Generators |
[311:6448:1] |
Generators of the group modulo torsion |
j |
61643918316527/73168088292 |
j-invariant |
L |
4.6400109501458 |
L(r)(E,1)/r! |
Ω |
0.20738163302617 |
Real period |
R |
3.7290436142928 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000051721 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bk1 29328p1 |
Quadratic twists by: -4 8 |