Atkin-Lehner |
2- 3- 5+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
85680dm |
Isogeny class |
Conductor |
85680 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-5828334704640000 = -1 · 214 · 314 · 54 · 7 · 17 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 2 4 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-194043,-33104342] |
[a1,a2,a3,a4,a6] |
Generators |
[71951:19299546:1] |
Generators of the group modulo torsion |
j |
-270601485933241/1951897500 |
j-invariant |
L |
6.5467718193691 |
L(r)(E,1)/r! |
Ω |
0.11368625426787 |
Real period |
R |
7.198288679582 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003674 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10710bc1 28560dr1 |
Quadratic twists by: -4 -3 |