Atkin-Lehner |
3- 7+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
3339a |
Isogeny class |
Conductor |
3339 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
384 |
Modular degree for the optimal curve |
Δ |
-2434131 = -1 · 38 · 7 · 53 |
Discriminant |
Eigenvalues |
0 3- 1 7+ -5 2 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-12,-77] |
[a1,a2,a3,a4,a6] |
Generators |
[7:13:1] |
Generators of the group modulo torsion |
j |
-262144/3339 |
j-invariant |
L |
2.9038976240365 |
L(r)(E,1)/r! |
Ω |
1.100663925554 |
Real period |
R |
0.65957863172786 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53424br1 1113a1 83475y1 23373e1 |
Quadratic twists by: -4 -3 5 -7 |