Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cl |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-9980928 = -1 · 210 · 33 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 0 -3 2 1 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-253,-1475] |
[a1,a2,a3,a4,a6] |
Generators |
[125:1380:1] |
Generators of the group modulo torsion |
j |
-4864000/27 |
j-invariant |
L |
5.0287677312793 |
L(r)(E,1)/r! |
Ω |
0.59813929490718 |
Real period |
R |
4.2036761116646 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000757 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312bm1 17328l1 69312cy1 |
Quadratic twists by: -4 8 -19 |