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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 28224.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.cu1 | 28224dn1 | \([0, 0, 0, -9555, 359464]\) | \(474552000/49\) | \(9961576128\) | \([2]\) | \(24576\) | \(0.95109\) | \(\Gamma_0(N)\)-optimal |
| 28224.cu2 | 28224dn2 | \([0, 0, 0, -8820, 417088]\) | \(-5832000/2401\) | \(-31239502737408\) | \([2]\) | \(49152\) | \(1.2977\) |
Rank
sage: E.rank()
The elliptic curves in class 28224.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.cu 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 LMFDB 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 LMFDB labels.
