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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 54720cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54720.bs2 | 54720cx1 | \([0, 0, 0, 5172, -98928]\) | \(2161700757/1848320\) | \(-13082201948160\) | \([2]\) | \(122880\) | \(1.2045\) | \(\Gamma_0(N)\)-optimal |
| 54720.bs1 | 54720cx2 | \([0, 0, 0, -25548, -873072]\) | \(260549802603/104256800\) | \(737917953638400\) | \([2]\) | \(245760\) | \(1.5510\) |
Rank
sage: E.rank()
The elliptic curves in class 54720cx have rank \(1\).
Complex multiplication
The elliptic curves in class 54720cx do not have complex multiplication.Modular form 54720.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
