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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 28224n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.ey2 | 28224n1 | \([0, 0, 0, -10584, 666792]\) | \(-55296/49\) | \(-116191823956992\) | \([2]\) | \(73728\) | \(1.3960\) | \(\Gamma_0(N)\)-optimal |
28224.ey1 | 28224n2 | \([0, 0, 0, -195804, 33339600]\) | \(21882096/7\) | \(265581311901696\) | \([2]\) | \(147456\) | \(1.7425\) |
Rank
sage: E.rank()
The elliptic curves in class 28224n have rank \(0\).
Complex multiplication
The elliptic curves in class 28224n do not have complex multiplication.Modular form 28224.2.a.n
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.