Atkin-Lehner |
2- 7+ 29- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12586g |
Isogeny class |
Conductor |
12586 |
Conductor |
∏ cp |
33 |
Product of Tamagawa factors cp |
deg |
13200 |
Modular degree for the optimal curve |
Δ |
-10838861824 = -1 · 211 · 7 · 293 · 31 |
Discriminant |
Eigenvalues |
2- 2 -1 7+ -3 4 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3646,-86405] |
[a1,a2,a3,a4,a6] |
Generators |
[97:647:1] |
Generators of the group modulo torsion |
j |
-5360201917525729/10838861824 |
j-invariant |
L |
8.8769691691728 |
L(r)(E,1)/r! |
Ω |
0.30715822459451 |
Real period |
R |
0.8757670939387 |
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 |
100688bi1 113274j1 88102m1 |
Quadratic twists by: -4 -3 -7 |