Atkin-Lehner |
3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
9975b |
Isogeny class |
Conductor |
9975 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
3753284032944140625 = 35 · 58 · 78 · 193 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7+ 0 -6 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-21722313,-38976858594] |
[a1,a2,a3,a4,a6] |
Generators |
[-322953631875021426:200398833266370712:119961748328759] |
Generators of the group modulo torsion |
j |
72547406094380206981321/240210178108425 |
j-invariant |
L |
1.8960686947116 |
L(r)(E,1)/r! |
Ω |
0.069931545132017 |
Real period |
R |
27.113210370688 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29925n1 1995g1 69825bx1 |
Quadratic twists by: -3 5 -7 |