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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 203280hj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.bc3 | 203280hj1 | \([0, -1, 0, -8631, -292950]\) | \(2508888064/118125\) | \(3348250290000\) | \([2]\) | \(491520\) | \(1.1641\) | \(\Gamma_0(N)\)-optimal |
| 203280.bc2 | 203280hj2 | \([0, -1, 0, -23756, 1032000]\) | \(3269383504/893025\) | \(405004355078400\) | \([2, 2]\) | \(983040\) | \(1.5107\) | |
| 203280.bc1 | 203280hj3 | \([0, -1, 0, -350456, 79962720]\) | \(2624033547076/324135\) | \(588006322928640\) | \([2]\) | \(1966080\) | \(1.8572\) | |
| 203280.bc4 | 203280hj4 | \([0, -1, 0, 60944, 6656080]\) | \(13799183324/18600435\) | \(-33742648554531840\) | \([2]\) | \(1966080\) | \(1.8572\) |
Rank
sage: E.rank()
The elliptic curves in class 203280hj have rank \(2\).
Complex multiplication
The elliptic curves in class 203280hj do not have complex multiplication.Modular form 203280.2.a.hj
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.
