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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 296208x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.x2 | 296208x1 | \([0, 0, 0, -231, -1210]\) | \(148176/17\) | \(156397824\) | \([2]\) | \(122880\) | \(0.30449\) | \(\Gamma_0(N)\)-optimal |
296208.x1 | 296208x2 | \([0, 0, 0, -891, 8954]\) | \(2125764/289\) | \(10635052032\) | \([2]\) | \(245760\) | \(0.65106\) |
Rank
sage: E.rank()
The elliptic curves in class 296208x have rank \(2\).
Complex multiplication
The elliptic curves in class 296208x do not have complex multiplication.Modular form 296208.2.a.x
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.