Atkin-Lehner |
2- 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
3486i |
Isogeny class |
Conductor |
3486 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
19200 |
Modular degree for the optimal curve |
Δ |
-1061158643564544 = -1 · 230 · 35 · 72 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- -3 4 2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,99,-1567245] |
[a1,a2,a3,a4,a6] |
Generators |
[375:-7356:1] |
Generators of the group modulo torsion |
j |
107239576751/1061158643564544 |
j-invariant |
L |
4.2380917094212 |
L(r)(E,1)/r! |
Ω |
0.22551050332268 |
Real period |
R |
0.31322204856515 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27888bf1 111552bs1 10458p1 87150bf1 |
Quadratic twists by: -4 8 -3 5 |