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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 270480fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.fq2 | 270480fq1 | \([0, 1, 0, -150936, -22171500]\) | \(789145184521/17996580\) | \(8672377407160320\) | \([2]\) | \(2211840\) | \(1.8448\) | \(\Gamma_0(N)\)-optimal |
| 270480.fq1 | 270480fq2 | \([0, 1, 0, -331256, 40796244]\) | \(8341959848041/3327411150\) | \(1603447170606489600\) | \([2]\) | \(4423680\) | \(2.1914\) |
Rank
sage: E.rank()
The elliptic curves in class 270480fq have rank \(2\).
Complex multiplication
The elliptic curves in class 270480fq do not have complex multiplication.Modular form 270480.2.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.
