Atkin-Lehner |
2+ 5+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
47120c |
Isogeny class |
Conductor |
47120 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
376832 |
Modular degree for the optimal curve |
Δ |
-1615980400000000 = -1 · 210 · 58 · 194 · 31 |
Discriminant |
Eigenvalues |
2+ 2 5+ 0 2 0 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-601656,-179436544] |
[a1,a2,a3,a4,a6] |
j |
-23521728535515140836/1578105859375 |
j-invariant |
L |
3.0855542638092 |
L(r)(E,1)/r! |
Ω |
0.085709840651174 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23560d1 |
Quadratic twists by: -4 |