Atkin-Lehner |
2+ 5- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440bu |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
1327104 |
Modular degree for the optimal curve |
Δ |
-3196787108085760000 = -1 · 236 · 54 · 74 · 31 |
Discriminant |
Eigenvalues |
2+ 2 5- 7- 2 -4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-173825,90490625] |
[a1,a2,a3,a4,a6] |
Generators |
[-125:10500:1] |
Generators of the group modulo torsion |
j |
-2215761453033409/12194775040000 |
j-invariant |
L |
9.9413255733616 |
L(r)(E,1)/r! |
Ω |
0.21806649079335 |
Real period |
R |
2.8492816392073 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999859 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440dl1 2170l1 |
Quadratic twists by: -4 8 |