Atkin-Lehner |
2- 3+ 13- 43- |
Signs for the Atkin-Lehner involutions |
Class |
53664j |
Isogeny class |
Conductor |
53664 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
4326396939072 = 26 · 32 · 133 · 434 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 0 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4778,80004] |
[a1,a2,a3,a4,a6] |
Generators |
[-70:258:1] [-16:390:1] |
Generators of the group modulo torsion |
j |
188526786904000/67599952173 |
j-invariant |
L |
8.2715984928651 |
L(r)(E,1)/r! |
Ω |
0.71232814105833 |
Real period |
R |
0.96767182801649 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
53664p1 107328cd2 |
Quadratic twists by: -4 8 |