Atkin-Lehner |
2- 3+ 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
61488k |
Isogeny class |
Conductor |
61488 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-8293076434944 = -1 · 221 · 33 · 74 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -1 7+ -2 2 -5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-33963,-2413094] |
[a1,a2,a3,a4,a6] |
Generators |
[213:128:1] [725:18816:1] |
Generators of the group modulo torsion |
j |
-39175823587347/74988032 |
j-invariant |
L |
9.4637171814981 |
L(r)(E,1)/r! |
Ω |
0.17581998149952 |
Real period |
R |
3.3641359690672 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7686m1 61488j1 |
Quadratic twists by: -4 -3 |