Atkin-Lehner |
2+ 3+ 7- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85008k |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
131328 |
Modular degree for the optimal curve |
Δ |
-141023511552 = -1 · 210 · 3 · 73 · 11 · 233 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7- 11- -3 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1224,7008] |
[a1,a2,a3,a4,a6] |
Generators |
[22:210:1] |
Generators of the group modulo torsion |
j |
197885122844/137718273 |
j-invariant |
L |
7.5808108411746 |
L(r)(E,1)/r! |
Ω |
0.65377328171397 |
Real period |
R |
1.932578934676 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009772 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42504f1 |
Quadratic twists by: -4 |