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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 162624.iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.iz1 | 162624gu2 | \([0, 1, 0, -57654241, -168474509953]\) | \(45637459887836881/13417633152\) | \(6231203670757283463168\) | \([2]\) | \(30965760\) | \(3.1610\) | |
| 162624.iz2 | 162624gu1 | \([0, 1, 0, -3136481, -3340214913]\) | \(-7347774183121/6119866368\) | \(-2842090951871154880512\) | \([2]\) | \(15482880\) | \(2.8144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162624.iz have rank \(1\).
Complex multiplication
The elliptic curves in class 162624.iz do not have complex multiplication.Modular form 162624.2.a.iz
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.
