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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 38808bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38808.s2 | 38808bx1 | \([0, 0, 0, 189, 13230]\) | \(108/11\) | \(-76046294016\) | \([2]\) | \(27648\) | \(0.76731\) | \(\Gamma_0(N)\)-optimal |
38808.s1 | 38808bx2 | \([0, 0, 0, -7371, 235494]\) | \(3203226/121\) | \(1673018468352\) | \([2]\) | \(55296\) | \(1.1139\) |
Rank
sage: E.rank()
The elliptic curves in class 38808bx have rank \(0\).
Complex multiplication
The elliptic curves in class 38808bx do not have complex multiplication.Modular form 38808.2.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.