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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 72128.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.bx1 | 72128bh2 | \([0, -1, 0, -3325793, 341474561]\) | \(263822189935250/149429406721\) | \(2304274631402314661888\) | \([2]\) | \(2949120\) | \(2.7890\) | |
72128.bx2 | 72128bh1 | \([0, -1, 0, 821567, 42035169]\) | \(7953970437500/4703287687\) | \(-36263499732606189568\) | \([2]\) | \(1474560\) | \(2.4425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 72128.bx do not have complex multiplication.Modular form 72128.2.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 LMFDB 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 LMFDB labels.