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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 14400cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.dw2 | 14400cw1 | \([0, 0, 0, -2700, -486000]\) | \(-108/5\) | \(-100776960000000\) | \([2]\) | \(36864\) | \(1.3670\) | \(\Gamma_0(N)\)-optimal |
14400.dw1 | 14400cw2 | \([0, 0, 0, -110700, -14094000]\) | \(3721734/25\) | \(1007769600000000\) | \([2]\) | \(73728\) | \(1.7136\) |
Rank
sage: E.rank()
The elliptic curves in class 14400cw have rank \(0\).
Complex multiplication
The elliptic curves in class 14400cw do not have complex multiplication.Modular form 14400.2.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 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.