Atkin-Lehner |
2+ 3+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042d |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
262080 |
Modular degree for the optimal curve |
Δ |
1303511460054804 = 22 · 33 · 78 · 115 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7+ 11- 13+ -7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-36922,-2122448] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:578:1] [-133:743:1] |
Generators of the group modulo torsion |
j |
965635947241/226115604 |
j-invariant |
L |
6.360559697754 |
L(r)(E,1)/r! |
Ω |
0.35023553691218 |
Real period |
R |
0.60536020548065 |
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 |
126126ei1 42042bn1 |
Quadratic twists by: -3 -7 |