Atkin-Lehner |
2+ 3- 5- 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
88110bm |
Isogeny class |
Conductor |
88110 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
456192 |
Modular degree for the optimal curve |
Δ |
-301088390625000 = -1 · 23 · 39 · 59 · 11 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 11- 2 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-49014,4271548] |
[a1,a2,a3,a4,a6] |
Generators |
[137:269:1] [-133:2969:1] |
Generators of the group modulo torsion |
j |
-17863296516440929/413015625000 |
j-invariant |
L |
8.4998864987209 |
L(r)(E,1)/r! |
Ω |
0.54524697606834 |
Real period |
R |
0.43302937690333 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996825 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
29370s1 |
Quadratic twists by: -3 |