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SageMath
E = EllipticCurve("to1")
E.isogeny_class()
Elliptic curves in class 435600.to
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.to1 | 435600to2 | \([0, 0, 0, -952875, 357706250]\) | \(1000188\) | \(95664294000000000\) | \([2]\) | \(6553600\) | \(2.1777\) | \(\Gamma_0(N)\)-optimal* |
435600.to2 | 435600to1 | \([0, 0, 0, -45375, 8318750]\) | \(-432\) | \(-23916073500000000\) | \([2]\) | \(3276800\) | \(1.8312\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435600.to have rank \(1\).
Complex multiplication
The elliptic curves in class 435600.to do not have complex multiplication.Modular form 435600.2.a.to
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.