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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 94864ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94864.cr2 | 94864ch1 | \([0, 1, 0, 15811, 884519]\) | \(8192/11\) | \(-586917422330624\) | \([]\) | \(345600\) | \(1.5196\) | \(\Gamma_0(N)\)-optimal |
94864.cr1 | 94864ch2 | \([0, 1, 0, -458509, 120033703]\) | \(-199794688/1331\) | \(-71017008102005504\) | \([]\) | \(1036800\) | \(2.0689\) |
Rank
sage: E.rank()
The elliptic curves in class 94864ch have rank \(0\).
Complex multiplication
The elliptic curves in class 94864ch do not have complex multiplication.Modular form 94864.2.a.ch
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.