Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312ct |
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+ -2 3 0 5 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,51,45] |
[a1,a2,a3,a4,a6] |
Generators |
[5:20:1] |
Generators of the group modulo torsion |
j |
38912/27 |
j-invariant |
L |
4.7956247204004 |
L(r)(E,1)/r! |
Ω |
1.4489975952717 |
Real period |
R |
1.6548076880724 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999981073 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312bu1 17328n1 69312dd1 |
Quadratic twists by: -4 8 -19 |