Atkin-Lehner |
2+ 5+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440d |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
3640655872000 = 227 · 53 · 7 · 31 |
Discriminant |
Eigenvalues |
2+ 3 5+ 7+ -1 5 -4 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18028,927152] |
[a1,a2,a3,a4,a6] |
Generators |
[183:24229:27] |
Generators of the group modulo torsion |
j |
2471874619761/13888000 |
j-invariant |
L |
10.991961633401 |
L(r)(E,1)/r! |
Ω |
0.79274950228984 |
Real period |
R |
6.9328089142538 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000828 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69440db1 2170o1 |
Quadratic twists by: -4 8 |