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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 286110.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.cw1 | 286110cw2 | \([1, -1, 0, -30587814, -65068280780]\) | \(179865548102096641/119964240000\) | \(2110925292868236240000\) | \([2]\) | \(24772608\) | \(3.0305\) | |
286110.cw2 | 286110cw1 | \([1, -1, 0, -2288934, -586452812]\) | \(75370704203521/35157196800\) | \(618636153169196236800\) | \([2]\) | \(12386304\) | \(2.6839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286110.cw have rank \(1\).
Complex multiplication
The elliptic curves in class 286110.cw do not have complex multiplication.Modular form 286110.2.a.cw
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.