Atkin-Lehner |
3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347m |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
436800 |
Modular degree for the optimal curve |
Δ |
-13006050586429329 = -1 · 32 · 116 · 138 |
Discriminant |
Eigenvalues |
-1 3+ -1 -2 11- 13+ 7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-204916,-36208138] |
[a1,a2,a3,a4,a6] |
j |
-658489/9 |
j-invariant |
L |
0.44841741695693 |
L(r)(E,1)/r! |
Ω |
0.11210435263326 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
507a1 61347i1 |
Quadratic twists by: -11 13 |