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SageMath
E = EllipticCurve("mx1")
E.isogeny_class()
Elliptic curves in class 273600.mx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.mx1 | 273600mx2 | \([0, 0, 0, -28778700, 59296934000]\) | \(882774443450089/2166000000\) | \(6467641344000000000000\) | \([2]\) | \(24772608\) | \(3.0633\) | |
273600.mx2 | 273600mx1 | \([0, 0, 0, -1130700, 1623206000]\) | \(-53540005609/350208000\) | \(-1045715484672000000000\) | \([2]\) | \(12386304\) | \(2.7167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.mx have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.mx do not have complex multiplication.Modular form 273600.2.a.mx
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.