Atkin-Lehner |
3- 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
32307f |
Isogeny class |
Conductor |
32307 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
36288 |
Modular degree for the optimal curve |
Δ |
259069833 = 37 · 113 · 89 |
Discriminant |
Eigenvalues |
-1 3- 2 0 11+ 2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-44602,-3629317] |
[a1,a2,a3,a4,a6] |
Generators |
[278:2201:1] |
Generators of the group modulo torsion |
j |
7372406363569883/194643 |
j-invariant |
L |
5.0845579881897 |
L(r)(E,1)/r! |
Ω |
0.32851932461286 |
Real period |
R |
4.4220560098874 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
96921k1 32307e1 |
Quadratic twists by: -3 -11 |