Atkin-Lehner |
2- 7+ 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
129584j |
Isogeny class |
Conductor |
129584 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
311040 |
Modular degree for the optimal curve |
Δ |
-453007003904 = -1 · 28 · 76 · 132 · 89 |
Discriminant |
Eigenvalues |
2- -1 3 7+ 0 13- -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-47164,-3926884] |
[a1,a2,a3,a4,a6] |
Generators |
[421257395:5532869888:1225043] |
Generators of the group modulo torsion |
j |
-45323646856802512/1769558609 |
j-invariant |
L |
7.3181629428493 |
L(r)(E,1)/r! |
Ω |
0.16198138822086 |
Real period |
R |
11.294759032775 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999934209 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32396c1 |
Quadratic twists by: -4 |