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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 159936.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.ee1 | 159936eo2 | \([0, -1, 0, -1143137, -10287423]\) | \(42852953779784/24786408969\) | \(95554641225117892608\) | \([2]\) | \(4423680\) | \(2.5233\) | |
| 159936.ee2 | 159936eo1 | \([0, -1, 0, 285703, -1428615]\) | \(5352028359488/3098832471\) | \(-1493297321495261184\) | \([2]\) | \(2211840\) | \(2.1768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 159936.ee do not have complex multiplication.Modular form 159936.2.a.ee
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.
