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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 128226.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128226.s1 | 128226ba3 | \([1, 0, 0, -7593771927, -254703853363449]\) | \(48427980631254958469835824847167473/153101623358112538524114\) | \(153101623358112538524114\) | \([]\) | \(151165440\) | \(4.0983\) | |
128226.s2 | 128226ba2 | \([1, 0, 0, -97056897, -323425585791]\) | \(101112050932948721991382242193/13327203141829750320519624\) | \(13327203141829750320519624\) | \([3]\) | \(50388480\) | \(3.5490\) | |
128226.s3 | 128226ba1 | \([1, 0, 0, -24080217, 45421448121]\) | \(1544204814149745316374461713/2295658741816117891584\) | \(2295658741816117891584\) | \([9]\) | \(16796160\) | \(2.9997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 128226.s have rank \(1\).
Complex multiplication
The elliptic curves in class 128226.s do not have complex multiplication.Modular form 128226.2.a.s
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.