Atkin-Lehner |
2+ 3- 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
61854k |
Isogeny class |
Conductor |
61854 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3386880 |
Modular degree for the optimal curve |
Δ |
6104673320464023552 = 220 · 32 · 139 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -4 -4 4 13+ -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-644908,-160070038] |
[a1,a2,a3,a4,a6] |
Generators |
[660969:-967265:729] |
Generators of the group modulo torsion |
j |
6145481607815809/1264743088128 |
j-invariant |
L |
2.7810576939831 |
L(r)(E,1)/r! |
Ω |
0.1709095223895 |
Real period |
R |
8.1360524987422 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002126 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4758i1 |
Quadratic twists by: 13 |