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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 16224.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16224.p1 | 16224v3 | \([0, 1, 0, -5464, 153596]\) | \(7301384/3\) | \(7413978624\) | \([2]\) | \(18432\) | \(0.85625\) | |
| 16224.p2 | 16224v2 | \([0, 1, 0, -2929, -60865]\) | \(140608/3\) | \(59311828992\) | \([2]\) | \(18432\) | \(0.85625\) | |
| 16224.p3 | 16224v1 | \([0, 1, 0, -394, 1496]\) | \(21952/9\) | \(2780241984\) | \([2, 2]\) | \(9216\) | \(0.50968\) | \(\Gamma_0(N)\)-optimal |
| 16224.p4 | 16224v4 | \([0, 1, 0, 1296, 12312]\) | \(97336/81\) | \(-200177422848\) | \([2]\) | \(18432\) | \(0.85625\) |
Rank
sage: E.rank()
The elliptic curves in class 16224.p have rank \(1\).
Complex multiplication
The elliptic curves in class 16224.p do not have complex multiplication.Modular form 16224.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
