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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 139650.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.bq1 | 139650ia2 | \([1, 1, 0, -83325, 14992125]\) | \(-1392225385/1316928\) | \(-60521586825000000\) | \([]\) | \(1555200\) | \(1.9165\) | |
139650.bq2 | 139650ia1 | \([1, 1, 0, 8550, -351000]\) | \(1503815/2052\) | \(-94303026562500\) | \([]\) | \(518400\) | \(1.3672\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 139650.bq do not have complex multiplication.Modular form 139650.2.a.bq
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.