Atkin-Lehner |
2- 3- 5+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
42300n |
Isogeny class |
Conductor |
42300 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
685260000000 = 28 · 36 · 57 · 47 |
Discriminant |
Eigenvalues |
2- 3- 5+ -1 1 5 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4575,-112250] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:50:1] |
Generators of the group modulo torsion |
j |
3631696/235 |
j-invariant |
L |
5.8308146437781 |
L(r)(E,1)/r! |
Ω |
0.58285640897294 |
Real period |
R |
0.83365510412934 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4700c1 8460e1 |
Quadratic twists by: -3 5 |