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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 139650bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.hs2 | 139650bo1 | \([1, 0, 0, -47188, 3534992]\) | \(6321363049/715008\) | \(1314374628000000\) | \([2]\) | \(983040\) | \(1.6336\) | \(\Gamma_0(N)\)-optimal |
139650.hs1 | 139650bo2 | \([1, 0, 0, -733188, 241576992]\) | \(23711636464489/363888\) | \(668922801750000\) | \([2]\) | \(1966080\) | \(1.9802\) |
Rank
sage: E.rank()
The elliptic curves in class 139650bo have rank \(0\).
Complex multiplication
The elliptic curves in class 139650bo do not have complex multiplication.Modular form 139650.2.a.bo
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 Cremona 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 Cremona labels.