Atkin-Lehner |
2- 5+ 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3230d |
Isogeny class |
Conductor |
3230 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
72646369280000 = 216 · 54 · 173 · 192 |
Discriminant |
Eigenvalues |
2- 0 5+ -2 2 2 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-65593,-6436519] |
[a1,a2,a3,a4,a6] |
Generators |
[-145:172:1] |
Generators of the group modulo torsion |
j |
31209728336698362849/72646369280000 |
j-invariant |
L |
4.4722430102267 |
L(r)(E,1)/r! |
Ω |
0.29836401444975 |
Real period |
R |
0.93682607352851 |
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 |
25840p1 103360s1 29070s1 16150i1 |
Quadratic twists by: -4 8 -3 5 |