Atkin-Lehner |
2- 3- 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
61488bh |
Isogeny class |
Conductor |
61488 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-114774866199576576 = -1 · 219 · 39 · 72 · 613 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ 0 -4 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-188859,35547626] |
[a1,a2,a3,a4,a6] |
Generators |
[365:3904:1] [109:4032:1] |
Generators of the group modulo torsion |
j |
-249487788397177/38437870464 |
j-invariant |
L |
8.0546172841003 |
L(r)(E,1)/r! |
Ω |
0.32104704269446 |
Real period |
R |
0.52267893622009 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999967 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7686x1 20496l1 |
Quadratic twists by: -4 -3 |