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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 115520cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115520.cx2 | 115520cw1 | \([0, -1, 0, -405, 3275]\) | \(318767104/125\) | \(2888000\) | \([]\) | \(36288\) | \(0.20435\) | \(\Gamma_0(N)\)-optimal |
115520.cx1 | 115520cw2 | \([0, -1, 0, -1165, -11013]\) | \(7575076864/1953125\) | \(45125000000\) | \([]\) | \(108864\) | \(0.75365\) |
Rank
sage: E.rank()
The elliptic curves in class 115520cw have rank \(0\).
Complex multiplication
The elliptic curves in class 115520cw do not have complex multiplication.Modular form 115520.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.