Atkin-Lehner |
2- 23- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
86848w |
Isogeny class |
Conductor |
86848 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
-8181776384 = -1 · 218 · 232 · 59 |
Discriminant |
Eigenvalues |
2- 1 3 -1 0 -4 -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3329,72959] |
[a1,a2,a3,a4,a6] |
Generators |
[65:368:1] |
Generators of the group modulo torsion |
j |
-15568817473/31211 |
j-invariant |
L |
9.176970749059 |
L(r)(E,1)/r! |
Ω |
1.3123862336563 |
Real period |
R |
1.7481459556804 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002649 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86848e1 21712j1 |
Quadratic twists by: -4 8 |