Atkin-Lehner |
2+ 7+ 19- 31- |
Signs for the Atkin-Lehner involutions |
Class |
32984a |
Isogeny class |
Conductor |
32984 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8832 |
Modular degree for the optimal curve |
Δ |
-381031168 = -1 · 28 · 7 · 193 · 31 |
Discriminant |
Eigenvalues |
2+ -2 0 7+ 2 4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33,931] |
[a1,a2,a3,a4,a6] |
Generators |
[9:38:1] |
Generators of the group modulo torsion |
j |
-16000000/1488403 |
j-invariant |
L |
3.796799312796 |
L(r)(E,1)/r! |
Ω |
1.3919827780444 |
Real period |
R |
0.22730162163179 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
65968g1 |
Quadratic twists by: -4 |