Atkin-Lehner |
2+ 5- 7+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
12040b |
Isogeny class |
Conductor |
12040 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
12672 |
Modular degree for the optimal curve |
Δ |
-8428000000 = -1 · 28 · 56 · 72 · 43 |
Discriminant |
Eigenvalues |
2+ -2 5- 7+ -3 -5 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3185,68275] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:350:1] [-10:315:1] |
Generators of the group modulo torsion |
j |
-13962024825856/32921875 |
j-invariant |
L |
4.8143907167543 |
L(r)(E,1)/r! |
Ω |
1.3105594361018 |
Real period |
R |
0.076532054812696 |
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 |
24080e1 96320d1 108360bg1 60200o1 |
Quadratic twists by: -4 8 -3 5 |