Atkin-Lehner |
2- 3+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
32472k |
Isogeny class |
Conductor |
32472 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
18951550197389568 = 28 · 39 · 113 · 414 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11- 6 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-72495,-3546126] |
[a1,a2,a3,a4,a6] |
Generators |
[-195:1782:1] |
Generators of the group modulo torsion |
j |
8362124262000/3761087891 |
j-invariant |
L |
5.8286813688003 |
L(r)(E,1)/r! |
Ω |
0.30346738328354 |
Real period |
R |
1.6005787579029 |
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 |
64944b1 32472b1 |
Quadratic twists by: -4 -3 |