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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 32340.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.bk1 | 32340bl2 | \([0, 1, 0, -19420, 1034900]\) | \(26894628304/9075\) | \(273322156800\) | \([2]\) | \(69120\) | \(1.1666\) | |
32340.bk2 | 32340bl1 | \([0, 1, 0, -1045, 20600]\) | \(-67108864/61875\) | \(-116472510000\) | \([2]\) | \(34560\) | \(0.82005\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 32340.bk do not have complex multiplication.Modular form 32340.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.