Atkin-Lehner |
3+ 5+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
12675p |
Isogeny class |
Conductor |
12675 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
179712 |
Modular degree for the optimal curve |
Δ |
-2796108233115234375 = -1 · 33 · 510 · 139 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -2 0 13- 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-426813,133953906] |
[a1,a2,a3,a4,a6] |
j |
-51895117/16875 |
j-invariant |
L |
0.48161195538179 |
L(r)(E,1)/r! |
Ω |
0.2408059776909 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38025by1 2535m1 12675o1 |
Quadratic twists by: -3 5 13 |