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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 17600.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.x1 | 17600s2 | \([0, 1, 0, -1473, -25697]\) | \(-53969305/10648\) | \(-69782732800\) | \([]\) | \(20736\) | \(0.80380\) | |
17600.x2 | 17600s1 | \([0, 1, 0, 127, 223]\) | \(34295/22\) | \(-144179200\) | \([]\) | \(6912\) | \(0.25449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17600.x have rank \(0\).
Complex multiplication
The elliptic curves in class 17600.x do not have complex multiplication.Modular form 17600.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.