Atkin-Lehner |
2+ 5- 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69290f |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
56448 |
Modular degree for the optimal curve |
Δ |
-4545424000 = -1 · 27 · 53 · 132 · 412 |
Discriminant |
Eigenvalues |
2+ 0 5- -1 -3 13+ -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4094,101908] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:464:1] [27:89:1] |
Generators of the group modulo torsion |
j |
-44909703885969/26896000 |
j-invariant |
L |
7.6484331731164 |
L(r)(E,1)/r! |
Ω |
1.3610274735706 |
Real period |
R |
0.93660038973472 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69290q1 |
Quadratic twists by: 13 |