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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2736.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2736.d1 | 2736v3 | \([0, 0, 0, -12607491, -17230231550]\) | \(74220219816682217473/16416\) | \(49017913344\) | \([2]\) | \(46080\) | \(2.3439\) | |
| 2736.d2 | 2736v2 | \([0, 0, 0, -787971, -269220350]\) | \(18120364883707393/269485056\) | \(804678065455104\) | \([2, 2]\) | \(23040\) | \(1.9973\) | |
| 2736.d3 | 2736v4 | \([0, 0, 0, -764931, -285703166]\) | \(-16576888679672833/2216253521952\) | \(-6617697556492320768\) | \([2]\) | \(46080\) | \(2.3439\) | |
| 2736.d4 | 2736v1 | \([0, 0, 0, -50691, -3947006]\) | \(4824238966273/537919488\) | \(1606218984456192\) | \([2]\) | \(11520\) | \(1.6507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2736.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2736.d do not have complex multiplication.Modular form 2736.2.a.d
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.
