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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 12870.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12870.bq1 | 12870br2 | \([1, -1, 1, -19958, -1080219]\) | \(1205943158724121/1258400\) | \(917373600\) | \([2]\) | \(23040\) | \(1.0096\) | |
12870.bq2 | 12870br1 | \([1, -1, 1, -1238, -16923]\) | \(-287626699801/9518080\) | \(-6938680320\) | \([2]\) | \(11520\) | \(0.66303\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12870.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 12870.bq do not have complex multiplication.Modular form 12870.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.