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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 145728.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145728.fq1 | 145728cn4 | \([0, 0, 0, -12435564, -16878985648]\) | \(1112891236915770073/327888\) | \(62660372594688\) | \([2]\) | \(2359296\) | \(2.4518\) | |
| 145728.fq2 | 145728cn3 | \([0, 0, 0, -915564, -163410352]\) | \(444142553850073/196663299888\) | \(37582941878577266688\) | \([2]\) | \(2359296\) | \(2.4518\) | |
| 145728.fq3 | 145728cn2 | \([0, 0, 0, -777324, -263662000]\) | \(271808161065433/147476736\) | \(28183243140366336\) | \([2, 2]\) | \(1179648\) | \(2.1052\) | |
| 145728.fq4 | 145728cn1 | \([0, 0, 0, -40044, -5614000]\) | \(-37159393753/49741824\) | \(-9505810598068224\) | \([2]\) | \(589824\) | \(1.7586\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145728.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 145728.fq do not have complex multiplication.Modular form 145728.2.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 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.
