Atkin-Lehner |
3+ 5+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
61605a |
Isogeny class |
Conductor |
61605 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
196992 |
Modular degree for the optimal curve |
Δ |
-12815803412955 = -1 · 33 · 5 · 377 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 4 0 -1 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,4107,-139296] |
[a1,a2,a3,a4,a6] |
Generators |
[222:3422:1] |
Generators of the group modulo torsion |
j |
110592/185 |
j-invariant |
L |
3.1257360355695 |
L(r)(E,1)/r! |
Ω |
0.37359289942411 |
Real period |
R |
1.0458362699367 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000964 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61605b1 1665b1 |
Quadratic twists by: -3 37 |