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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 7350.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.cw1 | 7350co2 | \([1, 0, 0, -871613, 314735217]\) | \(-16591834777/98304\) | \(-433881982464000000\) | \([]\) | \(136080\) | \(2.2246\) | |
7350.cw2 | 7350co1 | \([1, 0, 0, 28762, 2305092]\) | \(596183/864\) | \(-3813415861500000\) | \([]\) | \(45360\) | \(1.6753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.cw do not have complex multiplication.Modular form 7350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.