Atkin-Lehner |
3+ 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
39039b |
Isogeny class |
Conductor |
39039 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
625152 |
Modular degree for the optimal curve |
Δ |
297743883634197 = 34 · 711 · 11 · 132 |
Discriminant |
Eigenvalues |
0 3+ -2 7+ 11+ 13+ 2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-5800019,-5374475299] |
[a1,a2,a3,a4,a6] |
Generators |
[631384343:625521226:226981] |
Generators of the group modulo torsion |
j |
127680722384510660804608/1761798128013 |
j-invariant |
L |
3.0078772498138 |
L(r)(E,1)/r! |
Ω |
0.097284173754018 |
Real period |
R |
15.459232132759 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117117bb1 39039n1 |
Quadratic twists by: -3 13 |