Atkin-Lehner |
2+ 3- 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
48576bb |
Isogeny class |
Conductor |
48576 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
1935360 |
Modular degree for the optimal curve |
Δ |
3288917636749983744 = 225 · 318 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 11+ -3 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-9170657,10685875839] |
[a1,a2,a3,a4,a6] |
Generators |
[1843:6912:1] [-1127:139968:1] |
Generators of the group modulo torsion |
j |
325375754708447065657/12546225115776 |
j-invariant |
L |
9.3259573696247 |
L(r)(E,1)/r! |
Ω |
0.23571141974191 |
Real period |
R |
0.54951595400452 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48576cx1 1518d1 |
Quadratic twists by: -4 8 |