Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
11172f |
Isogeny class |
Conductor |
11172 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
231840 |
Modular degree for the optimal curve |
Δ |
-111290728502016 = -1 · 28 · 34 · 710 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 3 -2 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6889269,-6957681471] |
[a1,a2,a3,a4,a6] |
Generators |
[7508264277938387193096:94808272078372767446799:2419590733710277499] |
Generators of the group modulo torsion |
j |
-500060830302208/1539 |
j-invariant |
L |
3.3136650294253 |
L(r)(E,1)/r! |
Ω |
0.046593600109366 |
Real period |
R |
35.559229396819 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
44688do1 33516h1 11172n1 |
Quadratic twists by: -4 -3 -7 |