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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 67032.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67032.ci1 | 67032bf4 | \([0, 0, 0, -1425459, -543596690]\) | \(1823652903746/328593657\) | \(57717152452801529856\) | \([2]\) | \(1966080\) | \(2.5109\) | |
67032.ci2 | 67032bf2 | \([0, 0, 0, -419979, 96894070]\) | \(93280467172/7800849\) | \(685105724658410496\) | \([2, 2]\) | \(983040\) | \(2.1643\) | |
67032.ci3 | 67032bf1 | \([0, 0, 0, -411159, 101475178]\) | \(350104249168/2793\) | \(61323462643968\) | \([2]\) | \(491520\) | \(1.8177\) | \(\Gamma_0(N)\)-optimal |
67032.ci4 | 67032bf3 | \([0, 0, 0, 444381, 444193918]\) | \(55251546334/517244049\) | \(-90853408139394926592\) | \([2]\) | \(1966080\) | \(2.5109\) |
Rank
sage: E.rank()
The elliptic curves in class 67032.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 67032.ci do not have complex multiplication.Modular form 67032.2.a.ci
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.