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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 450800.da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.da1 | 450800da1 | \([0, 0, 0, -57575, 4887750]\) | \(44851536/4025\) | \(1894148900000000\) | \([2]\) | \(1474560\) | \(1.6712\) | \(\Gamma_0(N)\)-optimal |
450800.da2 | 450800da2 | \([0, 0, 0, 64925, 22895250]\) | \(16078716/129605\) | \(-243966378320000000\) | \([2]\) | \(2949120\) | \(2.0177\) |
Rank
sage: E.rank()
The elliptic curves in class 450800.da have rank \(0\).
Complex multiplication
The elliptic curves in class 450800.da do not have complex multiplication.Modular form 450800.2.a.da
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 LMFDB 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 LMFDB labels.