Atkin-Lehner |
2+ 3+ 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042l |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7104 |
Modular degree for the optimal curve |
Δ |
84084 = 22 · 3 · 72 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- 11+ 13+ -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-39,-111] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:23:8] [-4:3:1] |
Generators of the group modulo torsion |
j |
139317577/1716 |
j-invariant |
L |
4.7491527521802 |
L(r)(E,1)/r! |
Ω |
1.9055332029399 |
Real period |
R |
1.2461479928171 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126126fr1 42042z1 |
Quadratic twists by: -3 -7 |