Atkin-Lehner |
3- 11+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977k |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
432000 |
Modular degree for the optimal curve |
Δ |
-87283128192579 = -1 · 36 · 11 · 174 · 194 |
Discriminant |
Eigenvalues |
2 3- 3 2 11+ 4 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-666021,-209209307] |
[a1,a2,a3,a4,a6] |
j |
-44818771954214268928/119729942651 |
j-invariant |
L |
8.3559822481229 |
L(r)(E,1)/r! |
Ω |
0.083559822481292 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
25 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3553c1 |
Quadratic twists by: -3 |