Atkin-Lehner |
2- 3- 19- 101+ |
Signs for the Atkin-Lehner involutions |
Class |
69084b |
Isogeny class |
Conductor |
69084 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
42624 |
Modular degree for the optimal curve |
Δ |
-36171277056 = -1 · 28 · 36 · 19 · 1012 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 -3 0 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-984,14996] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:81:1] [5:101:1] |
Generators of the group modulo torsion |
j |
-564600832/193819 |
j-invariant |
L |
8.3547957911873 |
L(r)(E,1)/r! |
Ω |
1.0921492023313 |
Real period |
R |
1.9124666696956 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7676a1 |
Quadratic twists by: -3 |