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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 207936bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 207936.ex3 | 207936bv1 | \([0, 0, 0, -1667820, -63322288]\) | \(57066625/32832\) | \(295179637510417416192\) | \([2]\) | \(6635520\) | \(2.6174\) | \(\Gamma_0(N)\)-optimal |
| 207936.ex4 | 207936bv2 | \([0, 0, 0, 6649620, -505810096]\) | \(3616805375/2105352\) | \(-18928394255355516813312\) | \([2]\) | \(13271040\) | \(2.9640\) | |
| 207936.ex1 | 207936bv3 | \([0, 0, 0, -89000940, 323174021456]\) | \(8671983378625/82308\) | \(739998952369865883648\) | \([2]\) | \(19906560\) | \(3.1667\) | |
| 207936.ex2 | 207936bv4 | \([0, 0, 0, -86921580, 338992960592]\) | \(-8078253774625/846825858\) | \(-7613479221457365143912448\) | \([2]\) | \(39813120\) | \(3.5133\) |
Rank
sage: E.rank()
The elliptic curves in class 207936bv have rank \(0\).
Complex multiplication
The elliptic curves in class 207936bv do not have complex multiplication.Modular form 207936.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
