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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 185150cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185150.y2 | 185150cp1 | \([1, 1, 0, -185425, -7936875]\) | \(304821217/164864\) | \(381340450064000000\) | \([2]\) | \(2703360\) | \(2.0645\) | \(\Gamma_0(N)\)-optimal |
185150.y1 | 185150cp2 | \([1, 1, 0, -2301425, -1343132875]\) | \(582810602977/829472\) | \(1918619139384500000\) | \([2]\) | \(5406720\) | \(2.4111\) |
Rank
sage: E.rank()
The elliptic curves in class 185150cp have rank \(0\).
Complex multiplication
The elliptic curves in class 185150cp do not have complex multiplication.Modular form 185150.2.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.