Atkin-Lehner |
2+ 11+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
128986b |
Isogeny class |
Conductor |
128986 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2509056 |
Modular degree for the optimal curve |
Δ |
-2573897972332544 = -1 · 211 · 119 · 13 · 41 |
Discriminant |
Eigenvalues |
2+ -3 -1 2 11+ 13+ 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-548455,-156218243] |
[a1,a2,a3,a4,a6] |
Generators |
[1007733675:46015567807:421875] |
Generators of the group modulo torsion |
j |
-7737719666139/1091584 |
j-invariant |
L |
2.908334465825 |
L(r)(E,1)/r! |
Ω |
0.087716358964702 |
Real period |
R |
16.578061276451 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000406064 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128986t1 |
Quadratic twists by: -11 |