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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 152592bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.i2 | 152592bq1 | \([0, -1, 0, -1223144, 26145648]\) | \(2046931732873/1181672448\) | \(116828980219899543552\) | \([2]\) | \(3317760\) | \(2.5401\) | \(\Gamma_0(N)\)-optimal |
152592.i1 | 152592bq2 | \([0, -1, 0, -13800424, 19686949744]\) | \(2940001530995593/8673562656\) | \(857533305180255289344\) | \([2]\) | \(6635520\) | \(2.8867\) |
Rank
sage: E.rank()
The elliptic curves in class 152592bq have rank \(0\).
Complex multiplication
The elliptic curves in class 152592bq do not have complex multiplication.Modular form 152592.2.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.