Atkin-Lehner |
3- 11+ 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977n |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
362880 |
Modular degree for the optimal curve |
Δ |
-8557530543194973219 = -1 · 311 · 11 · 173 · 197 |
Discriminant |
Eigenvalues |
0 3- 2 1 11+ 1 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-682284,258578001] |
[a1,a2,a3,a4,a6] |
Generators |
[-487:21802:1] |
Generators of the group modulo torsion |
j |
-48182767872846856192/11738725024958811 |
j-invariant |
L |
5.4546137122604 |
L(r)(E,1)/r! |
Ω |
0.22130008556357 |
Real period |
R |
4.1080069312292 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10659j1 |
Quadratic twists by: -3 |