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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 4800.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.cp1 | 4800cr2 | \([0, 1, 0, -2153, -39177]\) | \(2156689088/81\) | \(41472000\) | \([2]\) | \(3072\) | \(0.54809\) | |
4800.cp2 | 4800cr1 | \([0, 1, 0, -128, -702]\) | \(-29218112/6561\) | \(-52488000\) | \([2]\) | \(1536\) | \(0.20152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.cp do not have complex multiplication.Modular form 4800.2.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.