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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9744.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9744.p1 | 9744w2 | \([0, 1, 0, -124, -88]\) | \(830321872/476847\) | \(122072832\) | \([2]\) | \(3072\) | \(0.24132\) | |
| 9744.p2 | 9744w1 | \([0, 1, 0, -89, -354]\) | \(4927700992/12789\) | \(204624\) | \([2]\) | \(1536\) | \(-0.10526\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9744.p have rank \(1\).
Complex multiplication
The elliptic curves in class 9744.p do not have complex multiplication.Modular form 9744.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
