Atkin-Lehner |
2+ 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
11328i |
Isogeny class |
Conductor |
11328 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
1276859554801385472 = 240 · 39 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -4 0 4 0 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1504705,-708854881] |
[a1,a2,a3,a4,a6] |
Generators |
[-679:504:1] |
Generators of the group modulo torsion |
j |
1437269372537979889/4870832652288 |
j-invariant |
L |
4.2826143706949 |
L(r)(E,1)/r! |
Ω |
0.1363405958815 |
Real period |
R |
3.4901273396362 |
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 |
11328n1 354e1 33984r1 |
Quadratic twists by: -4 8 -3 |