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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 159936bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.jj2 | 159936bz1 | \([0, 1, 0, 285703, 1428615]\) | \(5352028359488/3098832471\) | \(-1493297321495261184\) | \([2]\) | \(2211840\) | \(2.1768\) | \(\Gamma_0(N)\)-optimal |
| 159936.jj1 | 159936bz2 | \([0, 1, 0, -1143137, 10287423]\) | \(42852953779784/24786408969\) | \(95554641225117892608\) | \([2]\) | \(4423680\) | \(2.5233\) |
Rank
sage: E.rank()
The elliptic curves in class 159936bz have rank \(0\).
Complex multiplication
The elliptic curves in class 159936bz do not have complex multiplication.Modular form 159936.2.a.bz
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.
