Atkin-Lehner |
2+ 3- 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
7686f |
Isogeny class |
Conductor |
7686 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1920 |
Modular degree for the optimal curve |
Δ |
79688448 = 28 · 36 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 5 0 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-117,-203] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:19:1] |
Generators of the group modulo torsion |
j |
244140625/109312 |
j-invariant |
L |
3.2329189634055 |
L(r)(E,1)/r! |
Ω |
1.5129346493869 |
Real period |
R |
1.0684265062988 |
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 |
61488bt1 854c1 53802p1 |
Quadratic twists by: -4 -3 -7 |