Atkin-Lehner |
2- 5+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440cq |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
10763200 = 26 · 52 · 7 · 312 |
Discriminant |
Eigenvalues |
2- 0 5+ 7- -2 4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-223,1272] |
[a1,a2,a3,a4,a6] |
Generators |
[12:18:1] |
Generators of the group modulo torsion |
j |
19162771776/168175 |
j-invariant |
L |
5.1694005999103 |
L(r)(E,1)/r! |
Ω |
2.2893440371605 |
Real period |
R |
2.2580269789019 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000026 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440ci1 34720n2 |
Quadratic twists by: -4 8 |