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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 11550.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.cp1 | 11550ck2 | \([1, 0, 0, -2638, -49858]\) | \(129938649625/7072758\) | \(110511843750\) | \([2]\) | \(18432\) | \(0.87493\) | |
11550.cp2 | 11550ck1 | \([1, 0, 0, 112, -3108]\) | \(9938375/274428\) | \(-4287937500\) | \([2]\) | \(9216\) | \(0.52835\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.cp do not have complex multiplication.Modular form 11550.2.a.cp
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.