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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 273600bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.bx4 | 273600bx1 | \([0, 0, 0, 179700, -25558000]\) | \(214921799/218880\) | \(-653572177920000000\) | \([2]\) | \(4718592\) | \(2.1053\) | \(\Gamma_0(N)\)-optimal |
| 273600.bx3 | 273600bx2 | \([0, 0, 0, -972300, -235222000]\) | \(34043726521/11696400\) | \(34925263257600000000\) | \([2, 2]\) | \(9437184\) | \(2.4519\) | |
| 273600.bx2 | 273600bx3 | \([0, 0, 0, -6444300, 6123242000]\) | \(9912050027641/311647500\) | \(930574448640000000000\) | \([2]\) | \(18874368\) | \(2.7984\) | |
| 273600.bx1 | 273600bx4 | \([0, 0, 0, -13932300, -20012182000]\) | \(100162392144121/23457780\) | \(70044555755520000000\) | \([2]\) | \(18874368\) | \(2.7984\) |
Rank
sage: E.rank()
The elliptic curves in class 273600bx have rank \(1\).
Complex multiplication
The elliptic curves in class 273600bx do not have complex multiplication.Modular form 273600.2.a.bx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
