Atkin-Lehner |
2+ 3+ 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
48960p |
Isogeny class |
Conductor |
48960 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
-1891687307673600000 = -1 · 228 · 33 · 55 · 174 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 -2 0 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-579372,-182182864] |
[a1,a2,a3,a4,a6] |
j |
-3038732943445107/267267200000 |
j-invariant |
L |
1.7218138302078 |
L(r)(E,1)/r! |
Ω |
0.086090691520343 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48960dr1 1530i1 48960k1 |
Quadratic twists by: -4 8 -3 |