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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 59290bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.v1 | 59290bx1 | \([1, 1, 0, -6052, 492584]\) | \(-117649/440\) | \(-91705847239160\) | \([]\) | \(181440\) | \(1.3648\) | \(\Gamma_0(N)\)-optimal |
59290.v2 | 59290bx2 | \([1, 1, 0, 53238, -11733014]\) | \(80062991/332750\) | \(-69352546974614750\) | \([]\) | \(544320\) | \(1.9141\) |
Rank
sage: E.rank()
The elliptic curves in class 59290bx have rank \(0\).
Complex multiplication
The elliptic curves in class 59290bx do not have complex multiplication.Modular form 59290.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.