Atkin-Lehner |
2- 3- 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360df |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
1244160 |
Modular degree for the optimal curve |
Δ |
-403834805032950000 = -1 · 24 · 39 · 55 · 177 |
Discriminant |
Eigenvalues |
2- 3- 5+ -5 -5 0 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-49226,-30878601] |
[a1,a2,a3,a4,a6] |
Generators |
[487:7803:1] |
Generators of the group modulo torsion |
j |
-34158804736/1045659375 |
j-invariant |
L |
3.8818061034448 |
L(r)(E,1)/r! |
Ω |
0.13024534970906 |
Real period |
R |
0.82788327978708 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002204 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17340b1 4080x1 |
Quadratic twists by: -4 17 |