Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
11172g |
Isogeny class |
Conductor |
11172 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
261502408295955792 = 24 · 310 · 79 · 193 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- -4 -2 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-756429,252275598] |
[a1,a2,a3,a4,a6] |
Generators |
[231:9477:1] |
Generators of the group modulo torsion |
j |
74135539941376/405017091 |
j-invariant |
L |
2.9384476737903 |
L(r)(E,1)/r! |
Ω |
0.3122025297054 |
Real period |
R |
3.1373306259061 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
44688dp1 33516i1 11172u1 |
Quadratic twists by: -4 -3 -7 |