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SageMath
E = EllipticCurve("ij1")
E.isogeny_class()
Elliptic curves in class 141120ij
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.ix3 | 141120ij1 | \([0, 0, 0, -99372, -7611856]\) | \(4826809/1680\) | \(37771564359352320\) | \([2]\) | \(1179648\) | \(1.8824\) | \(\Gamma_0(N)\)-optimal |
| 141120.ix2 | 141120ij2 | \([0, 0, 0, -663852, 202600496]\) | \(1439069689/44100\) | \(991503564432998400\) | \([2, 2]\) | \(2359296\) | \(2.2290\) | |
| 141120.ix1 | 141120ij3 | \([0, 0, 0, -10542252, 13174915376]\) | \(5763259856089/5670\) | \(127479029712814080\) | \([2]\) | \(4718592\) | \(2.5756\) | |
| 141120.ix4 | 141120ij4 | \([0, 0, 0, 182868, 683876144]\) | \(30080231/9003750\) | \(-202431977738403840000\) | \([2]\) | \(4718592\) | \(2.5756\) |
Rank
sage: E.rank()
The elliptic curves in class 141120ij have rank \(0\).
Complex multiplication
The elliptic curves in class 141120ij do not have complex multiplication.Modular form 141120.2.a.ij
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 Cremona 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 Cremona labels.
