Atkin-Lehner |
2+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
123200cf |
Isogeny class |
Conductor |
123200 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
-10353112000000000 = -1 · 212 · 59 · 76 · 11 |
Discriminant |
Eigenvalues |
2+ 2 5+ 7- 11- -2 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,22967,4700937] |
[a1,a2,a3,a4,a6] |
Generators |
[3:2184:1] |
Generators of the group modulo torsion |
j |
20933297216/161767375 |
j-invariant |
L |
11.663779858952 |
L(r)(E,1)/r! |
Ω |
0.29645351556572 |
Real period |
R |
3.278698355122 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000010877 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
123200f1 61600bn1 24640h1 |
Quadratic twists by: -4 8 5 |