Atkin-Lehner |
3+ 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
15717a |
Isogeny class |
Conductor |
15717 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-110382720839300403 = -1 · 310 · 137 · 313 |
Discriminant |
Eigenvalues |
2 3+ -2 -2 -1 13+ 8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-74754,-17790901] |
[a1,a2,a3,a4,a6] |
j |
-9571339399168/22868673867 |
j-invariant |
L |
1.6165723615292 |
L(r)(E,1)/r! |
Ω |
0.13471436346076 |
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 |
47151d1 1209a1 |
Quadratic twists by: -3 13 |