Atkin-Lehner |
2+ 5+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
8360a |
Isogeny class |
Conductor |
8360 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
836000000 = 28 · 56 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ -2 5+ 2 11+ -2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-236,64] |
[a1,a2,a3,a4,a6] |
Generators |
[0:8:1] |
Generators of the group modulo torsion |
j |
5702413264/3265625 |
j-invariant |
L |
2.7749424407127 |
L(r)(E,1)/r! |
Ω |
1.3565400755678 |
Real period |
R |
2.0456029944793 |
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 |
16720k1 66880bu1 75240bn1 41800o1 |
Quadratic twists by: -4 8 -3 5 |