Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bw |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
-719207337600221184 = -1 · 218 · 38 · 114 · 134 |
Discriminant |
Eigenvalues |
2- 3- -1 0 11+ 13+ -1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,168944,30885908] |
[a1,a2,a3,a4,a6] |
Generators |
[68:-6534:1] |
Generators of the group modulo torsion |
j |
4558438520831/6147814464 |
j-invariant |
L |
7.1792751257226 |
L(r)(E,1)/r! |
Ω |
0.19249016300105 |
Real period |
R |
1.1655263004279 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005681 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11154ba1 89232ci1 |
Quadratic twists by: -4 13 |