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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 70560.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.cx1 | 70560dy1 | \([0, 0, 0, -13377, -537824]\) | \(140608/15\) | \(28241068322880\) | \([2]\) | \(143360\) | \(1.3154\) | \(\Gamma_0(N)\)-optimal |
70560.cx2 | 70560dy2 | \([0, 0, 0, 17493, -2655506]\) | \(39304/225\) | \(-3388928198745600\) | \([2]\) | \(286720\) | \(1.6619\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.cx do not have complex multiplication.Modular form 70560.2.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 LMFDB 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 LMFDB labels.