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SageMath
E = EllipticCurve("bcw1")
E.isogeny_class()
Elliptic curves in class 235200bcw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.bcw2 | 235200bcw1 | \([0, 1, 0, -294408, -61412562]\) | \(69934528/225\) | \(9079561575000000\) | \([2]\) | \(2752512\) | \(1.9282\) | \(\Gamma_0(N)\)-optimal |
235200.bcw1 | 235200bcw2 | \([0, 1, 0, -423033, -2630937]\) | \(3241792/1875\) | \(4842432840000000000\) | \([2]\) | \(5505024\) | \(2.2748\) |
Rank
sage: E.rank()
The elliptic curves in class 235200bcw have rank \(1\).
Complex multiplication
The elliptic curves in class 235200bcw do not have complex multiplication.Modular form 235200.2.a.bcw
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.