Atkin-Lehner |
3- 19+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
15219b |
Isogeny class |
Conductor |
15219 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
618240 |
Modular degree for the optimal curve |
Δ |
-87880730571 = -1 · 38 · 19 · 893 |
Discriminant |
Eigenvalues |
-1 3- -3 4 5 -1 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-54993974,156985233144] |
[a1,a2,a3,a4,a6] |
j |
-25231408121333628493036057/120549699 |
j-invariant |
L |
1.407615110009 |
L(r)(E,1)/r! |
Ω |
0.35190377750225 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073d1 |
Quadratic twists by: -3 |