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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 409101.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.bx1 | 409101bx2 | \([1, 0, 1, -55371055, -158523172909]\) | \(262623524091319/134454573\) | \(9612006346648997569971\) | \([2]\) | \(38707200\) | \(3.1697\) | \(\Gamma_0(N)\)-optimal* |
409101.bx2 | 409101bx1 | \([1, 0, 1, -2869760, -3350345407]\) | \(-36561310759/46662561\) | \(-3335854054461174739647\) | \([2]\) | \(19353600\) | \(2.8231\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 409101.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 409101.bx do not have complex multiplication.Modular form 409101.2.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.