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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 138600.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.bd1 | 138600eo4 | \([0, 0, 0, -144052275, 471861256750]\) | \(14171198121996897746/4077720290568771\) | \(95125058938388289888000000\) | \([2]\) | \(47185920\) | \(3.6912\) | |
| 138600.bd2 | 138600eo2 | \([0, 0, 0, -132073275, 584140423750]\) | \(21843440425782779332/3100814593569\) | \(36167901419388816000000\) | \([2, 2]\) | \(23592960\) | \(3.3446\) | |
| 138600.bd3 | 138600eo1 | \([0, 0, 0, -132068775, 584182224250]\) | \(87364831012240243408/1760913\) | \(5134822308000000\) | \([2]\) | \(11796480\) | \(2.9980\) | \(\Gamma_0(N)\)-optimal |
| 138600.bd4 | 138600eo3 | \([0, 0, 0, -120166275, 693744358750]\) | \(-8226100326647904626/4152140742401883\) | \(-96861139238751126624000000\) | \([2]\) | \(47185920\) | \(3.6912\) |
Rank
sage: E.rank()
The elliptic curves in class 138600.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 138600.bd do not have complex multiplication.Modular form 138600.2.a.bd
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 LMFDB 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 LMFDB labels.
