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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 16704.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16704.ce1 | 16704cf2 | \([0, 0, 0, -262092, -51995248]\) | \(-10418796526321/82044596\) | \(-15678966460317696\) | \([]\) | \(115200\) | \(1.9362\) | |
16704.ce2 | 16704cf1 | \([0, 0, 0, 2868, 98192]\) | \(13651919/29696\) | \(-5674993975296\) | \([]\) | \(23040\) | \(1.1315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16704.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 16704.ce do not have complex multiplication.Modular form 16704.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.