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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 134640.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.bq1 | 134640dw2 | \([0, 0, 0, -49923, 4289922]\) | \(170676802323/158950\) | \(12814798233600\) | \([2]\) | \(442368\) | \(1.4379\) | |
134640.bq2 | 134640dw1 | \([0, 0, 0, -2403, 98658]\) | \(-19034163/41140\) | \(-3316771307520\) | \([2]\) | \(221184\) | \(1.0914\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134640.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 134640.bq do not have complex multiplication.Modular form 134640.2.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 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.