Atkin-Lehner |
2+ 5+ 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
69680d |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1896960 |
Modular degree for the optimal curve |
Δ |
-3455505371093750000 = -1 · 24 · 519 · 132 · 67 |
Discriminant |
Eigenvalues |
2+ 3 5+ 1 -6 13- 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-177823,-93978103] |
[a1,a2,a3,a4,a6] |
j |
-38865792523212981504/215969085693359375 |
j-invariant |
L |
5.2196839945397 |
L(r)(E,1)/r! |
Ω |
0.10439368023637 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
25 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34840i1 |
Quadratic twists by: -4 |