Atkin-Lehner |
2+ 3+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
40128n |
Isogeny class |
Conductor |
40128 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
12672 |
Modular degree for the optimal curve |
Δ |
-14486208 = -1 · 26 · 3 · 11 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 11- -7 -7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-199,1165] |
[a1,a2,a3,a4,a6] |
Generators |
[12:19:1] |
Generators of the group modulo torsion |
j |
-13686220288/226347 |
j-invariant |
L |
2.291628876589 |
L(r)(E,1)/r! |
Ω |
2.2266856494428 |
Real period |
R |
0.34305529044361 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40128r1 20064f1 120384ba1 |
Quadratic twists by: -4 8 -3 |