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SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 271950ih
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271950.ih3 | 271950ih1 | \([1, 0, 0, -239044688, -1422567307008]\) | \(821774646379511057449/38361600000\) | \(70518810600000000000\) | \([2]\) | \(39813120\) | \(3.2873\) | \(\Gamma_0(N)\)-optimal |
| 271950.ih2 | 271950ih2 | \([1, 0, 0, -239436688, -1417667699008]\) | \(825824067562227826729/5613755625000000\) | \(10319573992587890625000000\) | \([2, 2]\) | \(79626240\) | \(3.6339\) | |
| 271950.ih1 | 271950ih3 | \([1, 0, 0, -392561688, 616291675992]\) | \(3639478711331685826729/2016912141902025000\) | \(3707620259103614675390625000\) | \([2]\) | \(159252480\) | \(3.9805\) | |
| 271950.ih4 | 271950ih4 | \([1, 0, 0, -92583688, -3138050594008]\) | \(-47744008200656797609/2286529541015625000\) | \(-4203248655796051025390625000\) | \([2]\) | \(159252480\) | \(3.9805\) |
Rank
sage: E.rank()
The elliptic curves in class 271950ih have rank \(1\).
Complex multiplication
The elliptic curves in class 271950ih do not have complex multiplication.Modular form 271950.2.a.ih
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.
