Atkin-Lehner |
2+ 3- 5+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160x |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
71680 |
Modular degree for the optimal curve |
Δ |
-429309849600 = -1 · 212 · 310 · 52 · 71 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 -2 -4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,1719,16119] |
[a1,a2,a3,a4,a6] |
Generators |
[9:-180:1] [-1:120:1] |
Generators of the group modulo torsion |
j |
137068836416/104811975 |
j-invariant |
L |
10.847314694297 |
L(r)(E,1)/r! |
Ω |
0.6037247646616 |
Real period |
R |
0.89836588866391 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000023 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160g1 34080j1 |
Quadratic twists by: -4 8 |