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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 221760fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.mv1 | 221760fq1 | \([0, 0, 0, -14892, -646704]\) | \(51603494067/4336640\) | \(30694252216320\) | \([2]\) | \(491520\) | \(1.3297\) | \(\Gamma_0(N)\)-optimal |
| 221760.mv2 | 221760fq2 | \([0, 0, 0, 15828, -2969136]\) | \(61958108493/573927200\) | \(-4062192441753600\) | \([2]\) | \(983040\) | \(1.6763\) |
Rank
sage: E.rank()
The elliptic curves in class 221760fq have rank \(1\).
Complex multiplication
The elliptic curves in class 221760fq do not have complex multiplication.Modular form 221760.2.a.fq
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 Cremona 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 Cremona labels.
