Atkin-Lehner |
2+ 3+ 43- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
12126b |
Isogeny class |
Conductor |
12126 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
654804 = 22 · 34 · 43 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -2 0 -4 -3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-24,-36] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:6:1] [-3:6:1] |
Generators of the group modulo torsion |
j |
1630532233/654804 |
j-invariant |
L |
3.4441092709191 |
L(r)(E,1)/r! |
Ω |
2.2214155261293 |
Real period |
R |
0.38760299799944 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999951 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97008y1 36378l1 |
Quadratic twists by: -4 -3 |