Atkin-Lehner |
2- 3+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
12936o |
Isogeny class |
Conductor |
12936 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-2578111244016 = -1 · 24 · 3 · 79 · 113 |
Discriminant |
Eigenvalues |
2- 3+ -3 7- 11+ 5 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2172,87249] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:343:1] |
Generators of the group modulo torsion |
j |
-1755904/3993 |
j-invariant |
L |
3.0313001474068 |
L(r)(E,1)/r! |
Ω |
0.71975924564825 |
Real period |
R |
1.0528868388056 |
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 |
25872y1 103488eh1 38808bi1 12936y1 |
Quadratic twists by: -4 8 -3 -7 |