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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 381150de
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.de2 | 381150de1 | \([1, -1, 0, -13272, -249364]\) | \(59319/28\) | \(122043723070500\) | \([2]\) | \(1244160\) | \(1.3971\) | \(\Gamma_0(N)\)-optimal |
381150.de1 | 381150de2 | \([1, -1, 0, -176622, -28508914]\) | \(139798359/98\) | \(427153030746750\) | \([2]\) | \(2488320\) | \(1.7437\) |
Rank
sage: E.rank()
The elliptic curves in class 381150de have rank \(1\).
Complex multiplication
The elliptic curves in class 381150de do not have complex multiplication.Modular form 381150.2.a.de
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.