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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 171600.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
171600.ce1 | 171600ep2 | \([0, -1, 0, -5208, -107088]\) | \(244140625/61347\) | \(3926208000000\) | \([2]\) | \(294912\) | \(1.1265\) | |
171600.ce2 | 171600ep1 | \([0, -1, 0, 792, -11088]\) | \(857375/1287\) | \(-82368000000\) | \([2]\) | \(147456\) | \(0.77993\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 171600.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 171600.ce do not have complex multiplication.Modular form 171600.2.a.ce
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.