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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 185130fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.co1 | 185130fe1 | \([1, -1, 0, -103659, -15779835]\) | \(-2575296504243/765952000\) | \(-36637128658944000\) | \([]\) | \(1728000\) | \(1.8926\) | \(\Gamma_0(N)\)-optimal |
185130.co2 | 185130fe2 | \([1, -1, 0, 767541, 131956325]\) | \(1434104310933/1046272480\) | \(-36483139658687214240\) | \([]\) | \(5184000\) | \(2.4419\) |
Rank
sage: E.rank()
The elliptic curves in class 185130fe have rank \(0\).
Complex multiplication
The elliptic curves in class 185130fe do not have complex multiplication.Modular form 185130.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.