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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 163800cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163800.ci1 | 163800cp1 | \([0, 0, 0, -2175, -38750]\) | \(10536048/91\) | \(9828000000\) | \([2]\) | \(143360\) | \(0.74176\) | \(\Gamma_0(N)\)-optimal |
163800.ci2 | 163800cp2 | \([0, 0, 0, -675, -91250]\) | \(-78732/8281\) | \(-3577392000000\) | \([2]\) | \(286720\) | \(1.0883\) |
Rank
sage: E.rank()
The elliptic curves in class 163800cp have rank \(0\).
Complex multiplication
The elliptic curves in class 163800cp do not have complex multiplication.Modular form 163800.2.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.