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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 203280hg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.o1 | 203280hg1 | \([0, -1, 0, -37274816, 87605808336]\) | \(3157287870431675236/673876665\) | \(1222465145368642560\) | \([2]\) | \(11980800\) | \(2.8558\) | \(\Gamma_0(N)\)-optimal |
| 203280.o2 | 203280hg2 | \([0, -1, 0, -37144136, 88250426640]\) | \(-1562098599189850178/23071165962075\) | \(-83705810622340196505600\) | \([2]\) | \(23961600\) | \(3.2023\) |
Rank
sage: E.rank()
The elliptic curves in class 203280hg have rank \(0\).
Complex multiplication
The elliptic curves in class 203280hg do not have complex multiplication.Modular form 203280.2.a.hg
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.
