Atkin-Lehner |
2+ 3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
42042z |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
49728 |
Modular degree for the optimal curve |
Δ |
9892398516 = 22 · 3 · 78 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 3 7+ 11+ 13- 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1937,32288] |
[a1,a2,a3,a4,a6] |
Generators |
[29:12:1] |
Generators of the group modulo torsion |
j |
139317577/1716 |
j-invariant |
L |
6.9494334585837 |
L(r)(E,1)/r! |
Ω |
1.294746008303 |
Real period |
R |
2.6837053035947 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126126ep1 42042l1 |
Quadratic twists by: -3 -7 |