Atkin-Lehner |
3- 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117bj |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
65015808 |
Modular degree for the optimal curve |
Δ |
1.0476844329137E+24 |
Discriminant |
Eigenvalues |
0 3- -2 7- 11+ 13+ -2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-8821829406,318923184026632] |
[a1,a2,a3,a4,a6] |
Generators |
[54206:8403:1] |
Generators of the group modulo torsion |
j |
127680722384510660804608/1761798128013 |
j-invariant |
L |
2.7483784185009 |
L(r)(E,1)/r! |
Ω |
0.061998659912526 |
Real period |
R |
2.0149837588959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999161899 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39039n1 117117bb1 |
Quadratic twists by: -3 13 |