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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 300560bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
300560.bq2 | 300560bq1 | \([0, -1, 0, -15376931760, -632222462862400]\) | \(827813553991775477153/123566310400000000\) | \(60020598197883562675404800000000\) | \([2]\) | \(601620480\) | \(4.8221\) | \(\Gamma_0(N)\)-optimal |
300560.bq1 | 300560bq2 | \([0, -1, 0, -236435205040, -44249141940429888]\) | \(3009261308803109129809313/85820312500000000\) | \(41686010346225440000000000000000\) | \([2]\) | \(1203240960\) | \(5.1686\) |
Rank
sage: E.rank()
The elliptic curves in class 300560bq have rank \(1\).
Complex multiplication
The elliptic curves in class 300560bq do not have complex multiplication.Modular form 300560.2.a.bq
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.