Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
11172i |
Isogeny class |
Conductor |
11172 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
2160 |
Modular degree for the optimal curve |
Δ |
-10859184 = -1 · 24 · 36 · 72 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- 3 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9,162] |
[a1,a2,a3,a4,a6] |
Generators |
[9:27:1] |
Generators of the group modulo torsion |
j |
-114688/13851 |
j-invariant |
L |
4.7889319383601 |
L(r)(E,1)/r! |
Ω |
1.8670688494822 |
Real period |
R |
0.42749110365233 |
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 |
44688ds1 33516o1 11172o1 |
Quadratic twists by: -4 -3 -7 |