Atkin-Lehner |
2+ 3- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
31824b |
Isogeny class |
Conductor |
31824 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
12551221133568 = 28 · 310 · 132 · 173 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 -2 13+ 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1194015,-502183874] |
[a1,a2,a3,a4,a6] |
j |
1008754689437602000/67254057 |
j-invariant |
L |
1.1554125958247 |
L(r)(E,1)/r! |
Ω |
0.14442657447792 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15912k1 127296cr1 10608g1 |
Quadratic twists by: -4 8 -3 |