Atkin-Lehner |
2+ 3- 5- 17- |
Signs for the Atkin-Lehner involutions |
Class |
69360by |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
648 |
Product of Tamagawa factors cp |
deg |
808704 |
Modular degree for the optimal curve |
Δ |
-26303101488000000 = -1 · 210 · 39 · 56 · 174 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 -2 -3 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-594280,176308100] |
[a1,a2,a3,a4,a6] |
Generators |
[-890:1020:1] [368:-2754:1] |
Generators of the group modulo torsion |
j |
-271395189079204/307546875 |
j-invariant |
L |
11.973003263545 |
L(r)(E,1)/r! |
Ω |
0.37465978145032 |
Real period |
R |
0.049316360610509 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999608 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34680bo1 69360f1 |
Quadratic twists by: -4 17 |