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SageMath
E = EllipticCurve("jd1")
E.isogeny_class()
Elliptic curves in class 178752.jd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178752.jd1 | 178752ce4 | \([0, 1, 0, -633537, -161276865]\) | \(1823652903746/328593657\) | \(5067075112454455296\) | \([2]\) | \(3932160\) | \(2.3081\) | |
| 178752.jd2 | 178752ce2 | \([0, 1, 0, -186657, 28647135]\) | \(93280467172/7800849\) | \(60146455937089536\) | \([2, 2]\) | \(1966080\) | \(1.9616\) | |
| 178752.jd3 | 178752ce1 | \([0, 1, 0, -182737, 30005807]\) | \(350104249168/2793\) | \(5383678476288\) | \([2]\) | \(983040\) | \(1.6150\) | \(\Gamma_0(N)\)-optimal |
| 178752.jd4 | 178752ce3 | \([0, 1, 0, 197503, 131678847]\) | \(55251546334/517244049\) | \(-7976156544473628672\) | \([2]\) | \(3932160\) | \(2.3081\) |
Rank
sage: E.rank()
The elliptic curves in class 178752.jd have rank \(1\).
Complex multiplication
The elliptic curves in class 178752.jd do not have complex multiplication.Modular form 178752.2.a.jd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
