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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 13248.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13248.bq1 | 13248bq2 | \([0, 0, 0, -2028, -32560]\) | \(19307236/1587\) | \(75820105728\) | \([2]\) | \(16384\) | \(0.83010\) | |
13248.bq2 | 13248bq1 | \([0, 0, 0, 132, -2320]\) | \(21296/207\) | \(-2472394752\) | \([2]\) | \(8192\) | \(0.48353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13248.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 13248.bq do not have complex multiplication.Modular form 13248.2.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.