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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 273600.do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.do1 | 273600do2 | \([0, 0, 0, -335894700, 2369478814000]\) | \(1403607530712116449/39475350\) | \(117872763494400000000\) | \([2]\) | \(41287680\) | \(3.3618\) | |
273600.do2 | 273600do1 | \([0, 0, 0, -20966700, 37122046000]\) | \(-341370886042369/1817528220\) | \(-5427110184468480000000\) | \([2]\) | \(20643840\) | \(3.0152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.do have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.do do not have complex multiplication.Modular form 273600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.