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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 140790bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.x2 | 140790bq1 | \([1, 0, 1, 10822, 155756]\) | \(1075696074359/702000000\) | \(-91485342000000\) | \([3]\) | \(852768\) | \(1.3678\) | \(\Gamma_0(N)\)-optimal |
140790.x1 | 140790bq2 | \([1, 0, 1, -124553, -19771444]\) | \(-1639709351099641/345558220800\) | \(-45033492892876800\) | \([]\) | \(2558304\) | \(1.9171\) |
Rank
sage: E.rank()
The elliptic curves in class 140790bq have rank \(0\).
Complex multiplication
The elliptic curves in class 140790bq do not have complex multiplication.Modular form 140790.2.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 Cremona 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 Cremona labels.