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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 446292bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446292.bh2 | 446292bh1 | \([0, 0, 0, -41160, -3121643]\) | \(5619712000/184437\) | \(253095136942032\) | \([2]\) | \(1327104\) | \(1.5371\) | \(\Gamma_0(N)\)-optimal* |
446292.bh1 | 446292bh2 | \([0, 0, 0, -100695, 7963774]\) | \(5142706000/1728243\) | \(37945522753383168\) | \([2]\) | \(2654208\) | \(1.8837\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446292bh have rank \(1\).
Complex multiplication
The elliptic curves in class 446292bh do not have complex multiplication.Modular form 446292.2.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.