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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 10944ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10944.bq3 | 10944ci1 | \([0, 0, 0, -4620, 9232]\) | \(57066625/32832\) | \(6274292908032\) | \([2]\) | \(18432\) | \(1.1452\) | \(\Gamma_0(N)\)-optimal |
10944.bq4 | 10944ci2 | \([0, 0, 0, 18420, 73744]\) | \(3616805375/2105352\) | \(-402339032727552\) | \([2]\) | \(36864\) | \(1.4918\) | |
10944.bq1 | 10944ci3 | \([0, 0, 0, -246540, -47116784]\) | \(8671983378625/82308\) | \(15729303748608\) | \([2]\) | \(55296\) | \(1.6945\) | |
10944.bq2 | 10944ci4 | \([0, 0, 0, -240780, -49423088]\) | \(-8078253774625/846825858\) | \(-161830941617553408\) | \([2]\) | \(110592\) | \(2.0411\) |
Rank
sage: E.rank()
The elliptic curves in class 10944ci have rank \(0\).
Complex multiplication
The elliptic curves in class 10944ci do not have complex multiplication.Modular form 10944.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.