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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 266805dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266805.dv3 | 266805dv1 | \([1, -1, 0, -866717154, 9821408678703]\) | \(473897054735271721/779625\) | \(118456156298050349625\) | \([2]\) | \(53084160\) | \(3.5435\) | \(\Gamma_0(N)\)-optimal |
| 266805.dv2 | 266805dv2 | \([1, -1, 0, -866983959, 9815059626840]\) | \(474334834335054841/607815140625\) | \(92351380853867503826390625\) | \([2, 2]\) | \(106168320\) | \(3.8901\) | |
| 266805.dv4 | 266805dv3 | \([1, -1, 0, -633529584, 15219481717215]\) | \(-185077034913624841/551466161890875\) | \(-83789721809884786063084360875\) | \([2]\) | \(212336640\) | \(4.2367\) | |
| 266805.dv1 | 266805dv4 | \([1, -1, 0, -1104707214, 4004295015573]\) | \(981281029968144361/522287841796875\) | \(79356370332482949065185546875\) | \([2]\) | \(212336640\) | \(4.2367\) |
Rank
sage: E.rank()
The elliptic curves in class 266805dv have rank \(1\).
Complex multiplication
The elliptic curves in class 266805dv do not have complex multiplication.Modular form 266805.2.a.dv
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.
