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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 209814bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209814.bl3 | 209814bv1 | \([1, 0, 1, -13533732, -19163845934]\) | \(6411014266033/296208\) | \(12666202383643907472\) | \([2]\) | \(13271040\) | \(2.7407\) | \(\Gamma_0(N)\)-optimal |
| 209814.bl2 | 209814bv2 | \([1, 0, 1, -14233112, -17073538990]\) | \(7457162887153/1370924676\) | \(58622351182099914757284\) | \([2, 2]\) | \(26542080\) | \(3.0872\) | |
| 209814.bl1 | 209814bv3 | \([1, 0, 1, -67735682, 198862833530]\) | \(803760366578833/65593817586\) | \(2804868770121323045625474\) | \([2]\) | \(53084160\) | \(3.4338\) | |
| 209814.bl4 | 209814bv4 | \([1, 0, 1, 28079378, -99227469574]\) | \(57258048889007/132611470002\) | \(-5670622391825524398980418\) | \([2]\) | \(53084160\) | \(3.4338\) |
Rank
sage: E.rank()
The elliptic curves in class 209814bv have rank \(1\).
Complex multiplication
The elliptic curves in class 209814bv do not have complex multiplication.Modular form 209814.2.a.bv
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.
