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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 22800cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.z2 | 22800cp1 | \([0, -1, 0, 2632, -33168]\) | \(3936827539/3158028\) | \(-1616910336000\) | \([2]\) | \(32256\) | \(1.0305\) | \(\Gamma_0(N)\)-optimal |
22800.z1 | 22800cp2 | \([0, -1, 0, -12568, -276368]\) | \(428831641421/181752822\) | \(93057444864000\) | \([2]\) | \(64512\) | \(1.3771\) |
Rank
sage: E.rank()
The elliptic curves in class 22800cp have rank \(0\).
Complex multiplication
The elliptic curves in class 22800cp do not have complex multiplication.Modular form 22800.2.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 Cremona 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 Cremona labels.