Atkin-Lehner |
3+ 5+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61005d |
Isogeny class |
Conductor |
61005 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
322972976025 = 33 · 52 · 78 · 83 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- -4 -2 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1716,-1716] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:140:1] [-21:170:1] |
Generators of the group modulo torsion |
j |
4750104241/2745225 |
j-invariant |
L |
4.8844025198207 |
L(r)(E,1)/r! |
Ω |
0.81092484931754 |
Real period |
R |
3.0116246430959 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000028 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8715l1 |
Quadratic twists by: -7 |