Atkin-Lehner |
2+ 3- 5- 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090x |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
1288224 |
Modular degree for the optimal curve |
Δ |
-213320926796040 = -1 · 23 · 39 · 5 · 78 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ 4 2 7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3719028,2760218458] |
[a1,a2,a3,a4,a6] |
j |
-986796427339482361/37004040 |
j-invariant |
L |
3.7384136790085 |
L(r)(E,1)/r! |
Ω |
0.41537929841784 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69090b1 |
Quadratic twists by: -7 |