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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 485100.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.cw1 | 485100cw2 | \([0, 0, 0, -24773175, -47826119250]\) | \(-3704530032/33275\) | \(-15102667742847300000000\) | \([]\) | \(41803776\) | \(3.0791\) | |
485100.cw2 | 485100cw1 | \([0, 0, 0, 951825, -346344250]\) | \(153174672/171875\) | \(-107009118562500000000\) | \([]\) | \(13934592\) | \(2.5297\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 485100.cw do not have complex multiplication.Modular form 485100.2.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.