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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 199410bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
199410.s2 | 199410bq1 | \([1, 0, 1, -3619, -151894]\) | \(-217081801/285660\) | \(-6895137960540\) | \([2]\) | \(663552\) | \(1.1564\) | \(\Gamma_0(N)\)-optimal |
199410.s1 | 199410bq2 | \([1, 0, 1, -70089, -7144538]\) | \(1577505447721/838350\) | \(20235730971150\) | \([2]\) | \(1327104\) | \(1.5030\) |
Rank
sage: E.rank()
The elliptic curves in class 199410bq have rank \(1\).
Complex multiplication
The elliptic curves in class 199410bq do not have complex multiplication.Modular form 199410.2.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.