Atkin-Lehner |
2+ 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
72896k |
Isogeny class |
Conductor |
72896 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-19827712 = -1 · 210 · 172 · 67 |
Discriminant |
Eigenvalues |
2+ -2 0 2 2 6 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,67,67] |
[a1,a2,a3,a4,a6] |
Generators |
[298:1887:8] |
Generators of the group modulo torsion |
j |
32000000/19363 |
j-invariant |
L |
4.9261186695346 |
L(r)(E,1)/r! |
Ω |
1.3296772130763 |
Real period |
R |
3.7047477550901 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987735 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72896r1 9112d1 |
Quadratic twists by: -4 8 |