Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 162624.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.y1 | 162624cg3 | \([0, -1, 0, -309872449, -1488601497887]\) | \(14171198121996897746/4077720290568771\) | \(946854983851088612102111232\) | \([2]\) | \(88473600\) | \(3.8827\) | |
| 162624.y2 | 162624cg2 | \([0, -1, 0, -284104289, -1842846700671]\) | \(21843440425782779332/3100814593569\) | \(360007742403227891073024\) | \([2, 2]\) | \(44236800\) | \(3.5361\) | |
| 162624.y3 | 162624cg1 | \([0, -1, 0, -284094609, -1842978582927]\) | \(87364831012240243408/1760913\) | \(51110949604442112\) | \([2]\) | \(22118400\) | \(3.1895\) | \(\Gamma_0(N)\)-optimal |
| 162624.y4 | 162624cg4 | \([0, -1, 0, -258491009, -2188651593951]\) | \(-8226100326647904626/4152140742401883\) | \(-964135564836893130668507136\) | \([2]\) | \(88473600\) | \(3.8827\) |
Rank
sage: E.rank()
The elliptic curves in class 162624.y have rank \(0\).
Complex multiplication
The elliptic curves in class 162624.y do not have complex multiplication.Modular form 162624.2.a.y
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
