Atkin-Lehner |
2- 3- 5+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090bt |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
350 |
Product of Tamagawa factors cp |
deg |
1915200 |
Modular degree for the optimal curve |
Δ |
2640660922368000000 = 225 · 37 · 56 · 72 · 47 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 0 3 -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-2240631,1288376361] |
[a1,a2,a3,a4,a6] |
Generators |
[1686:47157:1] |
Generators of the group modulo torsion |
j |
25388594846798277036481/53891039232000000 |
j-invariant |
L |
12.018683196789 |
L(r)(E,1)/r! |
Ω |
0.25654746464896 |
Real period |
R |
0.13385084469787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998857 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69090bi1 |
Quadratic twists by: -7 |