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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 41280by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.p1 | 41280by1 | \([0, -1, 0, -9889761, 11943992961]\) | \(408076159454905367161/1190206406250000\) | \(312005468160000000000\) | \([2]\) | \(2027520\) | \(2.8030\) | \(\Gamma_0(N)\)-optimal |
41280.p2 | 41280by2 | \([0, -1, 0, -5889761, 21690392961]\) | \(-86193969101536367161/725294740213012500\) | \(-190131664378399948800000\) | \([2]\) | \(4055040\) | \(3.1495\) |
Rank
sage: E.rank()
The elliptic curves in class 41280by have rank \(0\).
Complex multiplication
The elliptic curves in class 41280by do not have complex multiplication.Modular form 41280.2.a.by
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.