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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 96192bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96192.a2 | 96192bb1 | \([0, 0, 0, 1428, -15280]\) | \(1685159/1503\) | \(-287227772928\) | \([2]\) | \(188416\) | \(0.88604\) | \(\Gamma_0(N)\)-optimal |
96192.a1 | 96192bb2 | \([0, 0, 0, -7212, -136240]\) | \(217081801/83667\) | \(15989012692992\) | \([2]\) | \(376832\) | \(1.2326\) |
Rank
sage: E.rank()
The elliptic curves in class 96192bb have rank \(2\).
Complex multiplication
The elliptic curves in class 96192bb do not have complex multiplication.Modular form 96192.2.a.bb
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.