Atkin-Lehner |
2+ 3+ 5- 89- |
Signs for the Atkin-Lehner involutions |
Class |
10680a |
Isogeny class |
Conductor |
10680 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
1167858000 = 24 · 38 · 53 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 -4 2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3735,89100] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:405:1] |
Generators of the group modulo torsion |
j |
360239905232896/72991125 |
j-invariant |
L |
3.8059111657114 |
L(r)(E,1)/r! |
Ω |
1.4979446598595 |
Real period |
R |
0.8469185072272 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21360e1 85440q1 32040g1 53400s1 |
Quadratic twists by: -4 8 -3 5 |