Atkin-Lehner |
2- 7+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
111188d |
Isogeny class |
Conductor |
111188 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
656640 |
Modular degree for the optimal curve |
Δ |
1611128724321424 = 24 · 72 · 112 · 198 |
Discriminant |
Eigenvalues |
2- 1 -3 7+ 11- 7 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-29722,390709] |
[a1,a2,a3,a4,a6] |
Generators |
[165:77:1] |
Generators of the group modulo torsion |
j |
10686208/5929 |
j-invariant |
L |
5.3645819836139 |
L(r)(E,1)/r! |
Ω |
0.41142578819696 |
Real period |
R |
3.2597506856954 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005336 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111188j1 |
Quadratic twists by: -19 |