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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 489762bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.bl2 | 489762bl1 | \([1, -1, 0, 52443, -21757163]\) | \(4533086375/60669952\) | \(-213482015080169472\) | \([2]\) | \(6322176\) | \(2.0060\) | \(\Gamma_0(N)\)-optimal* |
489762.bl1 | 489762bl2 | \([1, -1, 0, -920997, -318266987]\) | \(24553362849625/1755162752\) | \(6175967983139590272\) | \([2]\) | \(12644352\) | \(2.3525\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 489762bl have rank \(1\).
Complex multiplication
The elliptic curves in class 489762bl do not have complex multiplication.Modular form 489762.2.a.bl
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.