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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 148800.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148800.eb1 | 148800fh4 | \([0, -1, 0, -1016753633, 12479106475137]\) | \(28379906689597370652529/1357352437500\) | \(5559715584000000000000\) | \([2]\) | \(39813120\) | \(3.6498\) | |
| 148800.eb2 | 148800fh3 | \([0, -1, 0, -63441633, 195681355137]\) | \(-6894246873502147249/47925198774000\) | \(-196301614178304000000000\) | \([2]\) | \(19906560\) | \(3.3032\) | |
| 148800.eb3 | 148800fh2 | \([0, -1, 0, -13649633, 13952971137]\) | \(68663623745397169/19216056254400\) | \(78708966418022400000000\) | \([2]\) | \(13271040\) | \(3.1005\) | |
| 148800.eb4 | 148800fh1 | \([0, -1, 0, 2222367, 1429963137]\) | \(296354077829711/387386634240\) | \(-1586735653847040000000\) | \([2]\) | \(6635520\) | \(2.7539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148800.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 148800.eb do not have complex multiplication.Modular form 148800.2.a.eb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
