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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 160080.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.cu1 | 160080n2 | \([0, 1, 0, -22080, -1269900]\) | \(290656902035521/86293125\) | \(353456640000\) | \([2]\) | \(376832\) | \(1.1944\) | |
| 160080.cu2 | 160080n1 | \([0, 1, 0, -1200, -25452]\) | \(-46694890801/39169575\) | \(-160438579200\) | \([2]\) | \(188416\) | \(0.84787\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.cu do not have complex multiplication.Modular form 160080.2.a.cu
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.
