Atkin-Lehner |
2- 3+ 5+ 17- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
111690bd |
Isogeny class |
Conductor |
111690 |
Conductor |
∏ cp |
44 |
Product of Tamagawa factors cp |
deg |
578688 |
Modular degree for the optimal curve |
Δ |
-4252183050240 = -1 · 211 · 39 · 5 · 172 · 73 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -1 -2 0 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-412103,101928511] |
[a1,a2,a3,a4,a6] |
Generators |
[343:-1090:1] |
Generators of the group modulo torsion |
j |
-393231916501775883/216033280 |
j-invariant |
L |
9.2777985806653 |
L(r)(E,1)/r! |
Ω |
0.63944176968842 |
Real period |
R |
0.32975490156635 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000039385 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111690b1 |
Quadratic twists by: -3 |