Atkin-Lehner |
2+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
30272a |
Isogeny class |
Conductor |
30272 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
3200 |
Modular degree for the optimal curve |
Δ |
-30272 = -1 · 26 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 1 2 4 11+ -4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32,-82] |
[a1,a2,a3,a4,a6] |
Generators |
[40447:222446:1331] |
Generators of the group modulo torsion |
j |
-58411072/473 |
j-invariant |
L |
8.3271473089444 |
L(r)(E,1)/r! |
Ω |
1.0005689076867 |
Real period |
R |
8.322412624431 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30272q1 15136d1 |
Quadratic twists by: -4 8 |