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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 117600.gw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.gw1 | 117600cw2 | \([0, 1, 0, -40833, 2984463]\) | \(1000000/63\) | \(474360768000000\) | \([2]\) | \(442368\) | \(1.5671\) | |
117600.gw2 | 117600cw1 | \([0, 1, 0, 2042, 197588]\) | \(8000/147\) | \(-17294403000000\) | \([2]\) | \(221184\) | \(1.2206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117600.gw have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.gw do not have complex multiplication.Modular form 117600.2.a.gw
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.