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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 68400.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.eo1 | 68400fi2 | \([0, 0, 0, -5826675, 5413459250]\) | \(468898230633769/5540400\) | \(258492902400000000\) | \([2]\) | \(1769472\) | \(2.4912\) | |
68400.eo2 | 68400fi1 | \([0, 0, 0, -354675, 89203250]\) | \(-105756712489/12476160\) | \(-582087720960000000\) | \([2]\) | \(884736\) | \(2.1446\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68400.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 68400.eo do not have complex multiplication.Modular form 68400.2.a.eo
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.