Atkin-Lehner |
2- 3- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
11856bh |
Isogeny class |
Conductor |
11856 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-2709213404086665216 = -1 · 220 · 321 · 13 · 19 |
Discriminant |
Eigenvalues |
2- 3- -3 -3 0 13+ -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,189688,-72463884] |
[a1,a2,a3,a4,a6] |
Generators |
[316:4374:1] |
Generators of the group modulo torsion |
j |
184281206604333047/661429053732096 |
j-invariant |
L |
3.8266728910598 |
L(r)(E,1)/r! |
Ω |
0.13004281459762 |
Real period |
R |
0.70062509484175 |
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 |
1482b1 47424ct1 35568bo1 |
Quadratic twists by: -4 8 -3 |