Atkin-Lehner |
2+ 3+ 5- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
12870i |
Isogeny class |
Conductor |
12870 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
108864 |
Modular degree for the optimal curve |
Δ |
-52968936930624000 = -1 · 29 · 33 · 53 · 119 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -1 11- 13- 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-9984,11082240] |
[a1,a2,a3,a4,a6] |
j |
-4076600308125723/1961812478912000 |
j-invariant |
L |
1.7253653913119 |
L(r)(E,1)/r! |
Ω |
0.28756089855198 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
102960ck1 12870bd2 64350cw1 |
Quadratic twists by: -4 -3 5 |