Atkin-Lehner |
2+ 3+ 5- 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
9690f |
Isogeny class |
Conductor |
9690 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
552330000 = 24 · 32 · 54 · 17 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 -6 -6 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2017,34021] |
[a1,a2,a3,a4,a6] |
Generators |
[197:-2806:1] [-23:274:1] |
Generators of the group modulo torsion |
j |
908192259751321/552330000 |
j-invariant |
L |
3.8763859012108 |
L(r)(E,1)/r! |
Ω |
1.6227160678192 |
Real period |
R |
0.29860321670606 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
77520cs1 29070bh1 48450bs1 |
Quadratic twists by: -4 -3 5 |