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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 38025.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.bq1 | 38025y2 | \([0, 0, 1, -122263050, 642291370906]\) | \(-21752792449024/6591796875\) | \(-61248885274669647216796875\) | \([]\) | \(8626176\) | \(3.6620\) | |
38025.bq2 | 38025y1 | \([0, 0, 1, 11204700, -7496369969]\) | \(16742875136/12301875\) | \(-114305119654999482421875\) | \([]\) | \(2875392\) | \(3.1127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38025.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 38025.bq do not have complex multiplication.Modular form 38025.2.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.