Atkin-Lehner |
3+ 7+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
111573a |
Isogeny class |
Conductor |
111573 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
749568 |
Modular degree for the optimal curve |
Δ |
-7351112641472523 = -1 · 33 · 74 · 118 · 232 |
Discriminant |
Eigenvalues |
-2 3+ -2 7+ 11+ -3 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-31311,-4643718] |
[a1,a2,a3,a4,a6] |
Generators |
[800:21961:1] |
Generators of the group modulo torsion |
j |
-52367109451776/113395848049 |
j-invariant |
L |
1.9910842675726 |
L(r)(E,1)/r! |
Ω |
0.16810537562041 |
Real period |
R |
1.4805328996991 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999997679374 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111573b1 111573e1 |
Quadratic twists by: -3 -7 |