Atkin-Lehner |
2+ 7- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
52598j |
Isogeny class |
Conductor |
52598 |
Conductor |
∏ cp |
44 |
Product of Tamagawa factors cp |
deg |
608256 |
Modular degree for the optimal curve |
Δ |
386298461819452 = 22 · 711 · 132 · 172 |
Discriminant |
Eigenvalues |
2+ -1 -4 7- -6 13+ 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-97832,-11780780] |
[a1,a2,a3,a4,a6] |
Generators |
[-177:-83:1] [-184:274:1] |
Generators of the group modulo torsion |
j |
358323755795002729/1336672878268 |
j-invariant |
L |
4.240425921269 |
L(r)(E,1)/r! |
Ω |
0.27000771791046 |
Real period |
R |
0.35692800612601 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52598d1 |
Quadratic twists by: 17 |