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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 31200bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31200.bt2 | 31200bx1 | \([0, 1, 0, -2458, -21412]\) | \(1643032000/767637\) | \(767637000000\) | \([2]\) | \(46080\) | \(0.97496\) | \(\Gamma_0(N)\)-optimal |
31200.bt1 | 31200bx2 | \([0, 1, 0, -32833, -2299537]\) | \(61162984000/41067\) | \(2628288000000\) | \([2]\) | \(92160\) | \(1.3215\) |
Rank
sage: E.rank()
The elliptic curves in class 31200bx have rank \(1\).
Complex multiplication
The elliptic curves in class 31200bx do not have complex multiplication.Modular form 31200.2.a.bx
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.