Atkin-Lehner |
2+ 5- 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
69680h |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
143616 |
Modular degree for the optimal curve |
Δ |
-8846093750000 = -1 · 24 · 511 · 132 · 67 |
Discriminant |
Eigenvalues |
2+ -1 5- 5 4 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1440,-142025] |
[a1,a2,a3,a4,a6] |
Generators |
[810:8125:8] |
Generators of the group modulo torsion |
j |
20624792002304/552880859375 |
j-invariant |
L |
7.2455056264054 |
L(r)(E,1)/r! |
Ω |
0.35405033988946 |
Real period |
R |
0.93020999472671 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001064 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34840d1 |
Quadratic twists by: -4 |