Atkin-Lehner |
2+ 3- 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
7686g |
Isogeny class |
Conductor |
7686 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
67200 |
Modular degree for the optimal curve |
Δ |
-10853042556482784 = -1 · 25 · 39 · 710 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 3 7+ -4 0 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-50373,6650293] |
[a1,a2,a3,a4,a6] |
Generators |
[1364:150581:64] |
Generators of the group modulo torsion |
j |
-19390744433389393/14887575523296 |
j-invariant |
L |
3.61047290489 |
L(r)(E,1)/r! |
Ω |
0.37190960982723 |
Real period |
R |
2.426982800046 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61488bv1 2562j1 53802w1 |
Quadratic twists by: -4 -3 -7 |