Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312cz |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-9102606336 = -1 · 214 · 34 · 193 |
Discriminant |
Eigenvalues |
2- 3- 1 -1 1 4 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-405,5427] |
[a1,a2,a3,a4,a6] |
Generators |
[6:57:1] |
Generators of the group modulo torsion |
j |
-65536/81 |
j-invariant |
L |
8.6709985709072 |
L(r)(E,1)/r! |
Ω |
1.1747518587048 |
Real period |
R |
0.92264150371184 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996286 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312c1 17328p1 69312cd1 |
Quadratic twists by: -4 8 -19 |