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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 286110.ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.ez1 | 286110ez2 | \([1, -1, 1, -373298, -55981969]\) | \(326940373369/112003650\) | \(1970848460162473650\) | \([2]\) | \(4718592\) | \(2.2124\) | |
| 286110.ez2 | 286110ez1 | \([1, -1, 1, 68872, -6105193]\) | \(2053225511/2098140\) | \(-36919475286790140\) | \([2]\) | \(2359296\) | \(1.8658\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286110.ez have rank \(0\).
Complex multiplication
The elliptic curves in class 286110.ez do not have complex multiplication.Modular form 286110.2.a.ez
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.
