Atkin-Lehner |
2+ 3- 11- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
48906p |
Isogeny class |
Conductor |
48906 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
449280 |
Modular degree for the optimal curve |
Δ |
-1129601197131264 = -1 · 29 · 37 · 11 · 136 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -1 -4 11- 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-189270,31782132] |
[a1,a2,a3,a4,a6] |
Generators |
[211:993:1] |
Generators of the group modulo torsion |
j |
-1028591238942753121/1549521532416 |
j-invariant |
L |
2.3922774129121 |
L(r)(E,1)/r! |
Ω |
0.48835703822752 |
Real period |
R |
1.2246559513103 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999734 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16302s1 |
Quadratic twists by: -3 |