Atkin-Lehner |
2- 19- 67- |
Signs for the Atkin-Lehner involutions |
Class |
81472d |
Isogeny class |
Conductor |
81472 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12864 |
Modular degree for the optimal curve |
Δ |
-24767488 = -1 · 210 · 192 · 67 |
Discriminant |
Eigenvalues |
2- 0 -2 -2 6 0 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,64,-136] |
[a1,a2,a3,a4,a6] |
j |
28311552/24187 |
j-invariant |
L |
1.172259005837 |
L(r)(E,1)/r! |
Ω |
1.1722590033589 |
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 |
81472a1 20368b1 |
Quadratic twists by: -4 8 |