Atkin-Lehner |
2+ 3- 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
22320j |
Isogeny class |
Conductor |
22320 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
591360 |
Modular degree for the optimal curve |
Δ |
-878649120000000 = -1 · 211 · 311 · 57 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 3 3 -2 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-14754963,-21815004238] |
[a1,a2,a3,a4,a6] |
Generators |
[1097833889593:107277580977246:99252847] |
Generators of the group modulo torsion |
j |
-237947203935023980322/588515625 |
j-invariant |
L |
5.7324389187585 |
L(r)(E,1)/r! |
Ω |
0.038515454557803 |
Real period |
R |
18.604346568711 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11160e1 89280fz1 7440e1 111600bq1 |
Quadratic twists by: -4 8 -3 5 |