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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 303450.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.cp1 | 303450cp2 | \([1, 0, 1, -11328951, -14680505702]\) | \(-4928752745352265/1056964608\) | \(-34483883212800000000\) | \([]\) | \(18662400\) | \(2.7439\) | |
303450.cp2 | 303450cp1 | \([1, 0, 1, 50424, -69388202]\) | \(434602535/64012032\) | \(-2088417548700000000\) | \([3]\) | \(6220800\) | \(2.1946\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.cp have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.cp do not have complex multiplication.Modular form 303450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.