Atkin-Lehner |
3- 7+ 19+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
51471c |
Isogeny class |
Conductor |
51471 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
309760 |
Modular degree for the optimal curve |
Δ |
-32742498254067 = -1 · 316 · 72 · 192 · 43 |
Discriminant |
Eigenvalues |
2 3- 2 7+ -1 -5 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-104529,-13010697] |
[a1,a2,a3,a4,a6] |
j |
-173263295590838272/44914263723 |
j-invariant |
L |
4.2481865991314 |
L(r)(E,1)/r! |
Ω |
0.13275583125172 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17157e1 |
Quadratic twists by: -3 |