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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2736q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2736.c3 | 2736q1 | \([0, 0, 0, 96, -16]\) | \(32768/19\) | \(-56733696\) | \([]\) | \(576\) | \(0.17728\) | \(\Gamma_0(N)\)-optimal |
| 2736.c2 | 2736q2 | \([0, 0, 0, -1344, -20176]\) | \(-89915392/6859\) | \(-20480864256\) | \([]\) | \(1728\) | \(0.72659\) | |
| 2736.c1 | 2736q3 | \([0, 0, 0, -110784, -14192656]\) | \(-50357871050752/19\) | \(-56733696\) | \([]\) | \(5184\) | \(1.2759\) |
Rank
sage: E.rank()
The elliptic curves in class 2736q have rank \(1\).
Complex multiplication
The elliptic curves in class 2736q do not have complex multiplication.Modular form 2736.2.a.q
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
