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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 187590a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187590.cq3 | 187590a1 | \([1, 0, 0, -32978410, 72891400100]\) | \(821774646379511057449/38361600000\) | \(185164116134400000\) | \([2]\) | \(13271040\) | \(2.7921\) | \(\Gamma_0(N)\)-optimal |
| 187590.cq2 | 187590a2 | \([1, 0, 0, -33032490, 72640328292]\) | \(825824067562227826729/5613755625000000\) | \(27096526174550625000000\) | \([2, 2]\) | \(26542080\) | \(3.1387\) | |
| 187590.cq4 | 187590a3 | \([1, 0, 0, -12772770, 160798473900]\) | \(-47744008200656797609/2286529541015625000\) | \(-11036641367340087890625000\) | \([2]\) | \(53084160\) | \(3.4853\) | |
| 187590.cq1 | 187590a4 | \([1, 0, 0, -54157490, -31586196708]\) | \(3639478711331685826729/2016912141902025000\) | \(9735249678741971388225000\) | \([2]\) | \(53084160\) | \(3.4853\) |
Rank
sage: E.rank()
The elliptic curves in class 187590a have rank \(1\).
Complex multiplication
The elliptic curves in class 187590a do not have complex multiplication.Modular form 187590.2.a.a
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.
