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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 23184by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.bq2 | 23184by1 | \([0, 0, 0, -2019, 8930]\) | \(304821217/164864\) | \(492281266176\) | \([2]\) | \(23040\) | \(0.93453\) | \(\Gamma_0(N)\)-optimal |
| 23184.bq1 | 23184by2 | \([0, 0, 0, -25059, 1524962]\) | \(582810602977/829472\) | \(2476790120448\) | \([2]\) | \(46080\) | \(1.2811\) |
Rank
sage: E.rank()
The elliptic curves in class 23184by have rank \(1\).
Complex multiplication
The elliptic curves in class 23184by do not have complex multiplication.Modular form 23184.2.a.by
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.
