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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 58800.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.bk1 | 58800cc1 | \([0, -1, 0, -1388, 15072]\) | \(78608/21\) | \(79060128000\) | \([2]\) | \(49152\) | \(0.79945\) | \(\Gamma_0(N)\)-optimal |
| 58800.bk2 | 58800cc2 | \([0, -1, 0, 3512, 93472]\) | \(318028/441\) | \(-6641050752000\) | \([2]\) | \(98304\) | \(1.1460\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.bk do not have complex multiplication.Modular form 58800.2.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.
