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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 14450.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.bg1 | 14450t4 | \([1, 0, 0, -906888, -332495608]\) | \(-349938025/8\) | \(-1885747578125000\) | \([]\) | \(151200\) | \(2.0445\) | |
14450.bg2 | 14450t3 | \([1, 0, 0, -3763, -1048733]\) | \(-25/2\) | \(-471436894531250\) | \([]\) | \(50400\) | \(1.4952\) | |
14450.bg3 | 14450t1 | \([1, 0, 0, -873, 11897]\) | \(-121945/32\) | \(-19310055200\) | \([]\) | \(10080\) | \(0.69051\) | \(\Gamma_0(N)\)-optimal |
14450.bg4 | 14450t2 | \([1, 0, 0, 6352, -87808]\) | \(46969655/32768\) | \(-19773496524800\) | \([]\) | \(30240\) | \(1.2398\) |
Rank
sage: E.rank()
The elliptic curves in class 14450.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 14450.bg do not have complex multiplication.Modular form 14450.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.