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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 200400.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.bk1 | 200400j1 | \([0, 1, 0, -248, -3372]\) | \(-16539745/36072\) | \(-3693772800\) | \([]\) | \(141696\) | \(0.52461\) | \(\Gamma_0(N)\)-optimal |
| 200400.bk2 | 200400j2 | \([0, 1, 0, 2152, 72468]\) | \(10758425855/27944778\) | \(-2861545267200\) | \([]\) | \(425088\) | \(1.0739\) |
Rank
sage: E.rank()
The elliptic curves in class 200400.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 200400.bk do not have complex multiplication.Modular form 200400.2.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.
