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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 43350cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43350.cb1 | 43350cd1 | \([1, 1, 1, -18213, 593031]\) | \(1771561/612\) | \(230815503562500\) | \([2]\) | \(184320\) | \(1.4578\) | \(\Gamma_0(N)\)-optimal |
43350.cb2 | 43350cd2 | \([1, 1, 1, 54037, 4205531]\) | \(46268279/46818\) | \(-17657386022531250\) | \([2]\) | \(368640\) | \(1.8044\) |
Rank
sage: E.rank()
The elliptic curves in class 43350cd have rank \(0\).
Complex multiplication
The elliptic curves in class 43350cd do not have complex multiplication.Modular form 43350.2.a.cd
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.