Atkin-Lehner |
3+ 11+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977a |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
200448 |
Modular degree for the optimal curve |
Δ |
8154479104497 = 39 · 11 · 172 · 194 |
Discriminant |
Eigenvalues |
1 3+ -2 -2 11+ -2 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-806208,-278422669] |
[a1,a2,a3,a4,a6] |
Generators |
[211316638:65428062253:2197] |
Generators of the group modulo torsion |
j |
2944245586351592979/414290459 |
j-invariant |
L |
3.8292297985151 |
L(r)(E,1)/r! |
Ω |
0.15932640511667 |
Real period |
R |
12.016934028326 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31977e1 |
Quadratic twists by: -3 |