Atkin-Lehner |
3- 5+ 7+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
109725bk |
Isogeny class |
Conductor |
109725 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
7055660390625 = 32 · 57 · 7 · 11 · 194 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 11+ -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-4813,-14008] |
[a1,a2,a3,a4,a6] |
Generators |
[-43:359:1] [-4:74:1] |
Generators of the group modulo torsion |
j |
789145184521/451562265 |
j-invariant |
L |
8.790988562718 |
L(r)(E,1)/r! |
Ω |
0.62126917599003 |
Real period |
R |
7.0750239204521 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000432 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21945m1 |
Quadratic twists by: 5 |