Atkin-Lehner |
2- 5+ 29+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68150p |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-1363000000 = -1 · 26 · 56 · 29 · 47 |
Discriminant |
Eigenvalues |
2- 2 5+ 1 -1 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,12,1781] |
[a1,a2,a3,a4,a6] |
Generators |
[15:67:1] |
Generators of the group modulo torsion |
j |
12167/87232 |
j-invariant |
L |
15.329825611396 |
L(r)(E,1)/r! |
Ω |
1.1986446771556 |
Real period |
R |
1.0657749472497 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000389 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2726b1 |
Quadratic twists by: 5 |