Atkin-Lehner |
2- 3+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bc |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
-836960256 = -1 · 216 · 33 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3+ -3 3 11+ -2 7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5619,-162126] |
[a1,a2,a3,a4,a6] |
j |
-177409591659/7568 |
j-invariant |
L |
2.2056859396258 |
L(r)(E,1)/r! |
Ω |
0.27571074352839 |
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 |
8514a1 68112bh1 |
Quadratic twists by: -4 -3 |