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SageMath
E = EllipticCurve("ow1")
E.isogeny_class()
Elliptic curves in class 141120.ow
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.ow1 | 141120ka3 | \([0, 0, 0, -3062892, 1942384304]\) | \(282678688658/18600435\) | \(209097478486443294720\) | \([2]\) | \(4718592\) | \(2.6487\) | |
| 141120.ow2 | 141120ka2 | \([0, 0, 0, -593292, -138994576]\) | \(4108974916/893025\) | \(5019486794942054400\) | \([2, 2]\) | \(2359296\) | \(2.3022\) | |
| 141120.ow3 | 141120ka1 | \([0, 0, 0, -558012, -160430704]\) | \(13674725584/945\) | \(1327906559508480\) | \([2]\) | \(1179648\) | \(1.9556\) | \(\Gamma_0(N)\)-optimal |
| 141120.ow4 | 141120ka4 | \([0, 0, 0, 1311828, -848461264]\) | \(22208984782/40516875\) | \(-455471949911408640000\) | \([2]\) | \(4718592\) | \(2.6487\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.ow have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.ow do not have complex multiplication.Modular form 141120.2.a.ow
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.
