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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 5775.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5775.y1 | 5775f2 | \([0, -1, 1, -669758, -3988338457]\) | \(-2126464142970105856/438611057788643355\) | \(-6853297777947552421875\) | \([]\) | \(720000\) | \(2.8692\) | |
5775.y2 | 5775f1 | \([0, -1, 1, -223508, 47704043]\) | \(-79028701534867456/16987307596875\) | \(-265426681201171875\) | \([]\) | \(144000\) | \(2.0645\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5775.y have rank \(0\).
Complex multiplication
The elliptic curves in class 5775.y do not have complex multiplication.Modular form 5775.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.