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SageMath
E = EllipticCurve("ix1")
E.isogeny_class()
Elliptic curves in class 58800.ix
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.ix1 | 58800ig1 | \([0, 1, 0, -692533, 221586938]\) | \(1248870793216/42525\) | \(1250755931250000\) | \([2]\) | \(552960\) | \(1.9886\) | \(\Gamma_0(N)\)-optimal |
58800.ix2 | 58800ig2 | \([0, 1, 0, -661908, 242105688]\) | \(-68150496976/14467005\) | \(-6808114684980000000\) | \([2]\) | \(1105920\) | \(2.3351\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.ix have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.ix do not have complex multiplication.Modular form 58800.2.a.ix
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.