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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 7650.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7650.ci1 | 7650by4 | \([1, -1, 1, -25430, 1084947]\) | \(159661140625/48275138\) | \(549883993781250\) | \([2]\) | \(41472\) | \(1.5335\) | |
7650.ci2 | 7650by3 | \([1, -1, 1, -23180, 1363947]\) | \(120920208625/19652\) | \(223848562500\) | \([2]\) | \(20736\) | \(1.1869\) | |
7650.ci3 | 7650by2 | \([1, -1, 1, -9680, -364053]\) | \(8805624625/2312\) | \(26335125000\) | \([2]\) | \(13824\) | \(0.98421\) | |
7650.ci4 | 7650by1 | \([1, -1, 1, -680, -4053]\) | \(3048625/1088\) | \(12393000000\) | \([2]\) | \(6912\) | \(0.63763\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7650.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 7650.ci do not have complex multiplication.Modular form 7650.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.