Atkin-Lehner |
2- 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
12688d |
Isogeny class |
Conductor |
12688 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
Δ |
-131320690731553024 = -1 · 28 · 1310 · 612 |
Discriminant |
Eigenvalues |
2- 0 2 -2 6 13+ -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-103919,-21685030] |
[a1,a2,a3,a4,a6] |
Generators |
[11681481585737113331520850:547353947704920195981591273:5200781528553462125000] |
Generators of the group modulo torsion |
j |
-484806711672241488/512971448170129 |
j-invariant |
L |
4.9869412748548 |
L(r)(E,1)/r! |
Ω |
0.12759240006005 |
Real period |
R |
39.084939796632 |
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 |
3172a2 50752j2 114192br2 |
Quadratic twists by: -4 8 -3 |