Atkin-Lehner |
2+ 3- 13+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
32136d |
Isogeny class |
Conductor |
32136 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
32640 |
Modular degree for the optimal curve |
Δ |
-20241052416 = -1 · 28 · 310 · 13 · 103 |
Discriminant |
Eigenvalues |
2+ 3- -3 -2 0 13+ -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3297,72099] |
[a1,a2,a3,a4,a6] |
Generators |
[15:-162:1] [-39:378:1] |
Generators of the group modulo torsion |
j |
-15487178564608/79066611 |
j-invariant |
L |
8.1936183193753 |
L(r)(E,1)/r! |
Ω |
1.2218421488049 |
Real period |
R |
0.16764887197968 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64272b1 96408o1 |
Quadratic twists by: -4 -3 |