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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 286650.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ce1 | 286650ce2 | \([1, -1, 0, -446463117, -3629259378459]\) | \(58753624886834093/30539798016\) | \(5115781273351203000000000\) | \([2]\) | \(92897280\) | \(3.6920\) | |
| 286650.ce2 | 286650ce1 | \([1, -1, 0, -23103117, -76845618459]\) | \(-8141222941613/10520100864\) | \(-1762242663347712000000000\) | \([2]\) | \(46448640\) | \(3.3455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.ce do not have complex multiplication.Modular form 286650.2.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.
