Atkin-Lehner |
7- 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12397b |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-10209462571 = -1 · 79 · 11 · 23 |
Discriminant |
Eigenvalues |
0 2 -3 7- 11+ -2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-947,-11915] |
[a1,a2,a3,a4,a6] |
j |
-799178752/86779 |
j-invariant |
L |
0.8553048464385 |
L(r)(E,1)/r! |
Ω |
0.42765242321925 |
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 |
111573bl1 1771c1 |
Quadratic twists by: -3 -7 |