Atkin-Lehner |
3+ 11+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977b |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-769270689 = -1 · 39 · 112 · 17 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 3 1 11+ 0 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,214,514] |
[a1,a2,a3,a4,a6] |
Generators |
[1:26:1] |
Generators of the group modulo torsion |
j |
55306341/39083 |
j-invariant |
L |
4.6727249064285 |
L(r)(E,1)/r! |
Ω |
1.0116727360447 |
Real period |
R |
1.1547026869325 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
31977d1 |
Quadratic twists by: -3 |