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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 277350.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.bx1 | 277350bx4 | \([1, 0, 1, -38760626, -92252480602]\) | \(65202655558249/512820150\) | \(50651911671759958593750\) | \([2]\) | \(34062336\) | \(3.1848\) | |
277350.bx2 | 277350bx2 | \([1, 0, 1, -4091876, 798444398]\) | \(76711450249/41602500\) | \(4109132910094101562500\) | \([2, 2]\) | \(17031168\) | \(2.8382\) | |
277350.bx3 | 277350bx1 | \([1, 0, 1, -3167376, 2166704398]\) | \(35578826569/51600\) | \(5096598958256250000\) | \([2]\) | \(8515584\) | \(2.4917\) | \(\Gamma_0(N)\)-optimal |
277350.bx4 | 277350bx3 | \([1, 0, 1, 15784874, 6284427398]\) | \(4403686064471/2721093750\) | \(-268765960689294433593750\) | \([2]\) | \(34062336\) | \(3.1848\) |
Rank
sage: E.rank()
The elliptic curves in class 277350.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 277350.bx do not have complex multiplication.Modular form 277350.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.