Atkin-Lehner |
2+ 7+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
52598b |
Isogeny class |
Conductor |
52598 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
689920 |
Modular degree for the optimal curve |
Δ |
-8030050924418432 = -1 · 27 · 7 · 135 · 176 |
Discriminant |
Eigenvalues |
2+ -3 0 7+ 5 13+ 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-6412,4317520] |
[a1,a2,a3,a4,a6] |
Generators |
[285:4915:1] |
Generators of the group modulo torsion |
j |
-1207949625/332678528 |
j-invariant |
L |
2.1410970055054 |
L(r)(E,1)/r! |
Ω |
0.33790007507792 |
Real period |
R |
3.1682399079938 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997829 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
182e1 |
Quadratic twists by: 17 |