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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 72128bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.k2 | 72128bq1 | \([0, 1, 0, -12609, 496831]\) | \(7189057/644\) | \(19861590769664\) | \([2]\) | \(221184\) | \(1.2914\) | \(\Gamma_0(N)\)-optimal |
72128.k1 | 72128bq2 | \([0, 1, 0, -43969, -2996673]\) | \(304821217/51842\) | \(1598858056957952\) | \([2]\) | \(442368\) | \(1.6380\) |
Rank
sage: E.rank()
The elliptic curves in class 72128bq have rank \(1\).
Complex multiplication
The elliptic curves in class 72128bq do not have complex multiplication.Modular form 72128.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.