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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 283220.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283220.bg1 | 283220bg1 | \([0, 1, 0, -14109076, -20415473660]\) | \(-177953104/125\) | \(-218184506032949792000\) | \([]\) | \(13934592\) | \(2.8390\) | \(\Gamma_0(N)\)-optimal |
283220.bg2 | 283220bg2 | \([0, 1, 0, 13646484, -86684648716]\) | \(161017136/1953125\) | \(-3409132906764840500000000\) | \([]\) | \(41803776\) | \(3.3883\) |
Rank
sage: E.rank()
The elliptic curves in class 283220.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 283220.bg do not have complex multiplication.Modular form 283220.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.