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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 429429bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.bh2 | 429429bh1 | \([1, 0, 0, -11606116662, -481268101528917]\) | \(-6914490272402831/141776649\) | \(-3545104523803392582628803207\) | \([2]\) | \(434903040\) | \(4.4057\) | \(\Gamma_0(N)\)-optimal* |
429429.bh1 | 429429bh2 | \([1, 0, 0, -185698780407, -30800793778432380]\) | \(28322170269781231871/11907\) | \(297732806231913377225901\) | \([2]\) | \(869806080\) | \(4.7523\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 429429bh have rank \(1\).
Complex multiplication
The elliptic curves in class 429429bh do not have complex multiplication.Modular form 429429.2.a.bh
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.