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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 283920c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.c2 | 283920c1 | \([0, -1, 0, 31609704, -409545092880]\) | \(80414592731747/1714608000000\) | \(-74475763552013451264000000\) | \([2]\) | \(75479040\) | \(3.6447\) | \(\Gamma_0(N)\)-optimal |
| 283920.c1 | 283920c2 | \([0, -1, 0, -671430296, -6342077828880]\) | \(770684091365988253/45935634276000\) | \(1995261562381104369451008000\) | \([2]\) | \(150958080\) | \(3.9913\) |
Rank
sage: E.rank()
The elliptic curves in class 283920c have rank \(1\).
Complex multiplication
The elliptic curves in class 283920c do not have complex multiplication.Modular form 283920.2.a.c
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.
