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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5775.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5775.r1 | 5775k2 | \([1, 1, 0, -18200, 937125]\) | \(341385539669/160083\) | \(312662109375\) | \([2]\) | \(9600\) | \(1.1616\) | |
5775.r2 | 5775k1 | \([1, 1, 0, -1325, 9000]\) | \(131872229/56133\) | \(109634765625\) | \([2]\) | \(4800\) | \(0.81499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5775.r have rank \(1\).
Complex multiplication
The elliptic curves in class 5775.r do not have complex multiplication.Modular form 5775.2.a.r
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.