Atkin-Lehner |
2- 3- 5+ 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
18330bb |
Isogeny class |
Conductor |
18330 |
Conductor |
∏ cp |
672 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-26341939976601600 = -1 · 224 · 37 · 52 · 13 · 472 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 -4 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-320261,70168641] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:8647:1] |
Generators of the group modulo torsion |
j |
-3632753777288703591889/26341939976601600 |
j-invariant |
L |
8.3611930260594 |
L(r)(E,1)/r! |
Ω |
0.37800419409986 |
Real period |
R |
0.131662576459 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
54990p1 91650a1 |
Quadratic twists by: -3 5 |