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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 24150ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.cg2 | 24150ch1 | \([1, 0, 0, -12688, -549508]\) | \(14457238157881/49990500\) | \(781101562500\) | \([2]\) | \(55296\) | \(1.1450\) | \(\Gamma_0(N)\)-optimal |
24150.cg1 | 24150ch2 | \([1, 0, 0, -18438, -3258]\) | \(44365623586201/25674468750\) | \(401163574218750\) | \([2]\) | \(110592\) | \(1.4916\) |
Rank
sage: E.rank()
The elliptic curves in class 24150ch have rank \(0\).
Complex multiplication
The elliptic curves in class 24150ch do not have complex multiplication.Modular form 24150.2.a.ch
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.