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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 9450.do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.do1 | 9450dv2 | \([1, -1, 1, -7130, -229553]\) | \(362010675/686\) | \(75951776250\) | \([]\) | \(15552\) | \(0.97760\) | |
9450.do2 | 9450dv1 | \([1, -1, 1, -380, 2647]\) | \(492075/56\) | \(688905000\) | \([3]\) | \(5184\) | \(0.42829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.do have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.do do not have complex multiplication.Modular form 9450.2.a.do
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.