Atkin-Lehner |
2- 3+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
42042cp |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
290304 |
Modular degree for the optimal curve |
Δ |
-1537251272933376 = -1 · 214 · 3 · 76 · 112 · 133 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 11- 13- 8 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-16269,2041731] |
[a1,a2,a3,a4,a6] |
Generators |
[183:-2380:1] |
Generators of the group modulo torsion |
j |
-4047806261953/13066420224 |
j-invariant |
L |
7.21062408404 |
L(r)(E,1)/r! |
Ω |
0.41820442564007 |
Real period |
R |
0.41052058583009 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126126cg1 858l1 |
Quadratic twists by: -3 -7 |