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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 207025.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207025.bq1 | 207025bq2 | \([0, 1, 1, -441653, 112504669]\) | \(671088640/2197\) | \(31190218668351925\) | \([]\) | \(1741824\) | \(2.0303\) | |
207025.bq2 | 207025bq1 | \([0, 1, 1, -27603, -1648916]\) | \(163840/13\) | \(184557506913325\) | \([]\) | \(580608\) | \(1.4810\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 207025.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 207025.bq do not have complex multiplication.Modular form 207025.2.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.