Atkin-Lehner |
2+ 11+ 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85514a |
Isogeny class |
Conductor |
85514 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1709568 |
Modular degree for the optimal curve |
Δ |
-470441077621956584 = -1 · 23 · 116 · 137 · 232 |
Discriminant |
Eigenvalues |
2+ 1 3 -5 11+ 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-151597,40051312] |
[a1,a2,a3,a4,a6] |
Generators |
[6150:-115558:27] |
Generators of the group modulo torsion |
j |
-79823598306193/97464199976 |
j-invariant |
L |
4.7029386388218 |
L(r)(E,1)/r! |
Ω |
0.26751083359168 |
Real period |
R |
2.1975458766422 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009121 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6578e1 |
Quadratic twists by: 13 |