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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 236992.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.ce1 | 236992ce2 | \([0, -1, 0, -1151809, -461125695]\) | \(1431644/49\) | \(5783976700260319232\) | \([2]\) | \(3956736\) | \(2.3720\) | |
| 236992.ce2 | 236992ce1 | \([0, -1, 0, -178449, 19130129]\) | \(21296/7\) | \(206570596437868544\) | \([2]\) | \(1978368\) | \(2.0254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.ce do not have complex multiplication.Modular form 236992.2.a.ce
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.
