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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 266616.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266616.bx1 | 266616bx2 | \([0, 0, 0, -4661019, 3873121110]\) | \(50668941906/1127\) | \(249085480534603776\) | \([2]\) | \(4325376\) | \(2.4530\) | |
266616.bx2 | 266616bx1 | \([0, 0, 0, -280899, 65044782]\) | \(-22180932/3703\) | \(-409211860878277632\) | \([2]\) | \(2162688\) | \(2.1064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 266616.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 266616.bx do not have complex multiplication.Modular form 266616.2.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.