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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 141120.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.bq1 | 141120fa2 | \([0, 0, 0, -282828, -57896048]\) | \(-5452947409/250\) | \(-114709561344000\) | \([]\) | \(829440\) | \(1.7734\) | |
141120.bq2 | 141120fa1 | \([0, 0, 0, -588, -206192]\) | \(-49/40\) | \(-18353529815040\) | \([]\) | \(276480\) | \(1.2241\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.bq do not have complex multiplication.Modular form 141120.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.