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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 340032bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
340032.bq2 | 340032bq1 | \([0, -1, 0, -248193, 47729025]\) | \(-6449916994998625/8532911772\) | \(-2236851623559168\) | \([2]\) | \(2064384\) | \(1.8517\) | \(\Gamma_0(N)\)-optimal |
340032.bq1 | 340032bq2 | \([0, -1, 0, -3972353, 3048657153]\) | \(26444015547214434625/46191222\) | \(12108751699968\) | \([2]\) | \(4128768\) | \(2.1983\) |
Rank
sage: E.rank()
The elliptic curves in class 340032bq have rank \(1\).
Complex multiplication
The elliptic curves in class 340032bq do not have complex multiplication.Modular form 340032.2.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.