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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 433251.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433251.bh1 | 433251bh2 | \([1, -1, 0, -466677, -83646662]\) | \(104154702625/32188247\) | \(3473696489037509007\) | \([2]\) | \(6082560\) | \(2.2622\) | \(\Gamma_0(N)\)-optimal* |
433251.bh2 | 433251bh1 | \([1, -1, 0, 80838, -8856113]\) | \(541343375/625807\) | \(-67535941883231367\) | \([2]\) | \(3041280\) | \(1.9156\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433251.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 433251.bh do not have complex multiplication.Modular form 433251.2.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 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.