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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 28224cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.j2 | 28224cu1 | \([0, 0, 0, -2352, -178360]\) | \(-16384/147\) | \(-12910202661888\) | \([2]\) | \(73728\) | \(1.1983\) | \(\Gamma_0(N)\)-optimal |
28224.j1 | 28224cu2 | \([0, 0, 0, -64092, -6228880]\) | \(20720464/63\) | \(88527103967232\) | \([2]\) | \(147456\) | \(1.5448\) |
Rank
sage: E.rank()
The elliptic curves in class 28224cu have rank \(1\).
Complex multiplication
The elliptic curves in class 28224cu do not have complex multiplication.Modular form 28224.2.a.cu
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.