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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 206910.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206910.bq1 | 206910ct2 | \([1, -1, 0, -1762569, 901104925]\) | \(468898230633769/5540400\) | \(7155249135447600\) | \([2]\) | \(3317760\) | \(2.1922\) | |
| 206910.bq2 | 206910ct1 | \([1, -1, 0, -107289, 14868013]\) | \(-105756712489/12476160\) | \(-16112561016119040\) | \([2]\) | \(1658880\) | \(1.8457\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206910.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 206910.bq do not have complex multiplication.Modular form 206910.2.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.
