Atkin-Lehner |
2+ 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232a |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
688896 |
Modular degree for the optimal curve |
Δ |
-20012315252447232 = -1 · 211 · 32 · 113 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 11+ 13+ -4 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-44672,7730592] |
[a1,a2,a3,a4,a6] |
Generators |
[113:2028:1] |
Generators of the group modulo torsion |
j |
-5901506/11979 |
j-invariant |
L |
6.9090304429365 |
L(r)(E,1)/r! |
Ω |
0.34240540848795 |
Real period |
R |
1.6814937019206 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999832454 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
44616t1 89232i1 |
Quadratic twists by: -4 13 |