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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 58608bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58608.bo4 | 58608bq1 | \([0, 0, 0, -3281259, 1972979098]\) | \(1308451928740468777/194033737531392\) | \(579381635728936009728\) | \([2]\) | \(2949120\) | \(2.7086\) | \(\Gamma_0(N)\)-optimal |
58608.bo2 | 58608bq2 | \([0, 0, 0, -50467179, 137991112090]\) | \(4760617885089919932457/133756441657344\) | \(399394594685762666496\) | \([2, 2]\) | \(5898240\) | \(3.0552\) | |
58608.bo3 | 58608bq3 | \([0, 0, 0, -48439659, 149586498970]\) | \(-4209586785160189454377/801182513521564416\) | \(-2392318166455175001145344\) | \([2]\) | \(11796480\) | \(3.4018\) | |
58608.bo1 | 58608bq4 | \([0, 0, 0, -807469419, 8831556236698]\) | \(19499096390516434897995817/15393430272\) | \(45964536497307648\) | \([4]\) | \(11796480\) | \(3.4018\) |
Rank
sage: E.rank()
The elliptic curves in class 58608bq have rank \(1\).
Complex multiplication
The elliptic curves in class 58608bq do not have complex multiplication.Modular form 58608.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.