Atkin-Lehner |
2+ 3+ 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
114192d |
Isogeny class |
Conductor |
114192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-71255808 = -1 · 28 · 33 · 132 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 -4 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,9,406] |
[a1,a2,a3,a4,a6] |
Generators |
[5:24:1] [18:80:1] |
Generators of the group modulo torsion |
j |
11664/10309 |
j-invariant |
L |
9.9755648305596 |
L(r)(E,1)/r! |
Ω |
1.5197855961986 |
Real period |
R |
3.2818987275677 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001884 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57096b1 114192c1 |
Quadratic twists by: -4 -3 |