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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 26950.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26950.cj1 | 26950ce4 | \([1, -1, 1, -25613755, 49901510747]\) | \(1010962818911303721/57392720\) | \(105503064301250000\) | \([2]\) | \(1179648\) | \(2.7331\) | |
26950.cj2 | 26950ce3 | \([1, -1, 1, -2681755, -397969253]\) | \(1160306142246441/634128110000\) | \(1165695906459218750000\) | \([2]\) | \(1179648\) | \(2.7331\) | |
26950.cj3 | 26950ce2 | \([1, -1, 1, -1603755, 777050747]\) | \(248158561089321/1859334400\) | \(3417950512900000000\) | \([2, 2]\) | \(589824\) | \(2.3865\) | |
26950.cj4 | 26950ce1 | \([1, -1, 1, -35755, 27546747]\) | \(-2749884201/176619520\) | \(-324673592320000000\) | \([2]\) | \(294912\) | \(2.0399\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26950.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 26950.cj do not have complex multiplication.Modular form 26950.2.a.cj
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.