Atkin-Lehner |
2- 3+ 13- 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
75582t |
Isogeny class |
Conductor |
75582 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
373248 |
Modular degree for the optimal curve |
Δ |
-1033383873330432 = -1 · 28 · 39 · 133 · 173 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 2 0 5 13- 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-27164,2322271] |
[a1,a2,a3,a4,a6] |
Generators |
[13:1397:1] |
Generators of the group modulo torsion |
j |
-112615610706171/52501339904 |
j-invariant |
L |
13.054367293403 |
L(r)(E,1)/r! |
Ω |
0.45994611615013 |
Real period |
R |
0.5912996668841 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000553 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75582c1 |
Quadratic twists by: -3 |