Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8736i |
Isogeny class |
Conductor |
8736 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-27779641344 = -1 · 212 · 32 · 73 · 133 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- 4 13+ 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-15421,732011] |
[a1,a2,a3,a4,a6] |
Generators |
[77:84:1] |
Generators of the group modulo torsion |
j |
-99021508447744/6782139 |
j-invariant |
L |
5.1830573195551 |
L(r)(E,1)/r! |
Ω |
1.124817395113 |
Real period |
R |
0.38399249973626 |
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 |
8736m1 17472l1 26208bp1 61152j1 |
Quadratic twists by: -4 8 -3 -7 |