Atkin-Lehner |
2- 3+ 5- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
81840cb |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
192000 |
Modular degree for the optimal curve |
Δ |
-33940684800000 = -1 · 217 · 35 · 55 · 11 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 5- -3 11+ -1 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6160,-334400] |
[a1,a2,a3,a4,a6] |
Generators |
[120:800:1] |
Generators of the group modulo torsion |
j |
-6312136778641/8286300000 |
j-invariant |
L |
4.9474307078428 |
L(r)(E,1)/r! |
Ω |
0.25690140976645 |
Real period |
R |
0.96290454554469 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000692 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10230bh1 |
Quadratic twists by: -4 |