Atkin-Lehner |
2+ 3+ 5+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
85200f |
Isogeny class |
Conductor |
85200 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
675840 |
Modular degree for the optimal curve |
Δ |
-1676991600000000 = -1 · 210 · 310 · 58 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 4 -6 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-80408,9021312] |
[a1,a2,a3,a4,a6] |
Generators |
[158:-486:1] |
Generators of the group modulo torsion |
j |
-3593411145796/104811975 |
j-invariant |
L |
5.7847550349938 |
L(r)(E,1)/r! |
Ω |
0.47134132636163 |
Real period |
R |
1.5341204716433 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000020348 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42600bh1 17040e1 |
Quadratic twists by: -4 5 |