Atkin-Lehner |
2+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
722b |
Isogeny class |
Conductor |
722 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
120 |
Modular degree for the optimal curve |
Δ |
-54872 = -1 · 23 · 193 |
Discriminant |
Eigenvalues |
2+ -3 2 -3 -2 3 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1,-11] |
[a1,a2,a3,a4,a6] |
Generators |
[5:7:1] |
Generators of the group modulo torsion |
j |
-27/8 |
j-invariant |
L |
1.1653365367539 |
L(r)(E,1)/r! |
Ω |
1.5826710943294 |
Real period |
R |
0.36815499472039 |
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 |
5776j1 23104g1 6498t1 18050q1 |
Quadratic twists by: -4 8 -3 5 |