Atkin-Lehner |
2- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696bz |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-289232912384 = -1 · 221 · 13 · 1032 |
Discriminant |
Eigenvalues |
2- 3 -1 -5 -4 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1652,-1264] |
[a1,a2,a3,a4,a6] |
Generators |
[1056:9476:27] |
Generators of the group modulo torsion |
j |
1902014919/1103336 |
j-invariant |
L |
7.8353052676475 |
L(r)(E,1)/r! |
Ω |
0.5777948490797 |
Real period |
R |
3.3901761498732 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000216 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696i1 21424w1 |
Quadratic twists by: -4 8 |