Atkin-Lehner |
2+ 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360b |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
10967040 |
Modular degree for the optimal curve |
Δ |
-2.4809421475047E+24 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 1 -5 -2 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-43714236,134619486615] |
[a1,a2,a3,a4,a6] |
Generators |
[11191709395295509:2444782284663165187:230459146091] |
Generators of the group modulo torsion |
j |
-4868914236046592/1307544150375 |
j-invariant |
L |
3.7156744246203 |
L(r)(E,1)/r! |
Ω |
0.077363298451254 |
Real period |
R |
24.014451936544 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34680q1 69360bm1 |
Quadratic twists by: -4 17 |