Atkin-Lehner |
3- 5+ 7+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
81585j |
Isogeny class |
Conductor |
81585 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
20991686945355 = 39 · 5 · 78 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 5 -1 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-8168,-177208] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:79:1] |
Generators of the group modulo torsion |
j |
14338681/4995 |
j-invariant |
L |
3.4031426399172 |
L(r)(E,1)/r! |
Ω |
0.51652651769501 |
Real period |
R |
3.2942574400119 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999769528 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27195r1 81585bg1 |
Quadratic twists by: -3 -7 |