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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 26928bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.q2 | 26928bk1 | \([0, 0, 0, -38091, -141446]\) | \(2046931732873/1181672448\) | \(3528455022968832\) | \([2]\) | \(92160\) | \(1.6728\) | \(\Gamma_0(N)\)-optimal |
26928.q1 | 26928bk2 | \([0, 0, 0, -429771, -108166790]\) | \(2940001530995593/8673562656\) | \(25899119313813504\) | \([2]\) | \(184320\) | \(2.0194\) |
Rank
sage: E.rank()
The elliptic curves in class 26928bk have rank \(0\).
Complex multiplication
The elliptic curves in class 26928bk do not have complex multiplication.Modular form 26928.2.a.bk
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.