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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 5775.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5775.p1 | 5775y2 | \([0, 1, 1, -23583, -1400506]\) | \(3713464238080/4108797\) | \(1604998828125\) | \([]\) | \(12960\) | \(1.2567\) | |
5775.p2 | 5775y1 | \([0, 1, 1, -1083, 11369]\) | \(359956480/56133\) | \(21926953125\) | \([3]\) | \(4320\) | \(0.70737\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5775.p have rank \(0\).
Complex multiplication
The elliptic curves in class 5775.p do not have complex multiplication.Modular form 5775.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.