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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 328560b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
328560.b1 | 328560b1 | \([0, -1, 0, -415574096, -189406761024]\) | \(14910549714397/8599633920\) | \(4577785388416852042595696640\) | \([2]\) | \(165722112\) | \(3.9971\) | \(\Gamma_0(N)\)-optimal |
328560.b2 | 328560b2 | \([0, -1, 0, 1659172784, -1515584966720]\) | \(948905782000163/550998028800\) | \(-293309081380888342299515289600\) | \([2]\) | \(331444224\) | \(4.3437\) |
Rank
sage: E.rank()
The elliptic curves in class 328560b have rank \(1\).
Complex multiplication
The elliptic curves in class 328560b do not have complex multiplication.Modular form 328560.2.a.b
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.