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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 338100.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338100.bk1 | 338100bk2 | \([0, -1, 0, -739220533, -7735623302063]\) | \(-4651506434740759035904/3638671875\) | \(-34945804687500000000\) | \([]\) | \(83980800\) | \(3.4902\) | |
| 338100.bk2 | 338100bk1 | \([0, -1, 0, -8924533, -11099936063]\) | \(-8185177630572544/808255330875\) | \(-7762484197723500000000\) | \([]\) | \(27993600\) | \(2.9409\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338100.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 338100.bk do not have complex multiplication.Modular form 338100.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
