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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 308550.ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.ey1 | 308550ey1 | \([1, 0, 1, -267776, 45096698]\) | \(76711450249/12622500\) | \(349398886289062500\) | \([2]\) | \(5529600\) | \(2.0878\) | \(\Gamma_0(N)\)-optimal |
308550.ey2 | 308550ey2 | \([1, 0, 1, 488474, 253821698]\) | \(465664585751/1274620050\) | \(-35282299537469531250\) | \([2]\) | \(11059200\) | \(2.4344\) |
Rank
sage: E.rank()
The elliptic curves in class 308550.ey have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.ey do not have complex multiplication.Modular form 308550.2.a.ey
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.