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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 11550.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.ci1 | 11550cg3 | \([1, 0, 0, -5663, -164433]\) | \(1285429208617/614922\) | \(9608156250\) | \([2]\) | \(16384\) | \(0.87038\) | |
| 11550.ci2 | 11550cg4 | \([1, 0, 0, -3163, 67067]\) | \(223980311017/4278582\) | \(66852843750\) | \([2]\) | \(16384\) | \(0.87038\) | |
| 11550.ci3 | 11550cg2 | \([1, 0, 0, -413, -1683]\) | \(498677257/213444\) | \(3335062500\) | \([2, 2]\) | \(8192\) | \(0.52381\) | |
| 11550.ci4 | 11550cg1 | \([1, 0, 0, 87, -183]\) | \(4657463/3696\) | \(-57750000\) | \([2]\) | \(4096\) | \(0.17723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.ci do not have complex multiplication.Modular form 11550.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
