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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 337590.fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
337590.fe1 | 337590fe2 | \([1, -1, 1, -719852, -234898221]\) | \(31942518433489/27900\) | \(36031956335100\) | \([2]\) | \(3686400\) | \(1.9017\) | |
337590.fe2 | 337590fe1 | \([1, -1, 1, -44672, -3716589]\) | \(-7633736209/230640\) | \(-297864172370160\) | \([2]\) | \(1843200\) | \(1.5551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 337590.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 337590.fe do not have complex multiplication.Modular form 337590.2.a.fe
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.