Atkin-Lehner |
2- 5+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
122200u |
Isogeny class |
Conductor |
122200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
644352 |
Modular degree for the optimal curve |
Δ |
-763750000 = -1 · 24 · 57 · 13 · 47 |
Discriminant |
Eigenvalues |
2- -2 5+ -1 -4 13+ -2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-566008,163712613] |
[a1,a2,a3,a4,a6] |
Generators |
[-762:12375:1] [418:575:1] |
Generators of the group modulo torsion |
j |
-80214370475766016/3055 |
j-invariant |
L |
7.399331173573 |
L(r)(E,1)/r! |
Ω |
0.85596817947844 |
Real period |
R |
1.0805499773844 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999969664 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24440e1 |
Quadratic twists by: 5 |