Atkin-Lehner |
7- 37- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
85211k |
Isogeny class |
Conductor |
85211 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-491224458011 = -1 · 710 · 37 · 47 |
Discriminant |
Eigenvalues |
0 1 -3 7- -2 5 -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-16137,784375] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:1200:1] |
Generators of the group modulo torsion |
j |
-3950306394112/4175339 |
j-invariant |
L |
4.0467619652493 |
L(r)(E,1)/r! |
Ω |
0.92764299585183 |
Real period |
R |
1.0906032799951 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999974022 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12173d1 |
Quadratic twists by: -7 |