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SageMath
E = EllipticCurve("ix1")
E.isogeny_class()
Elliptic curves in class 346560.ix
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.ix1 | 346560ix2 | \([0, 1, 0, -37394305, 88001560703]\) | \(468898230633769/5540400\) | \(68328619794078105600\) | \([2]\) | \(26542080\) | \(2.9559\) | |
| 346560.ix2 | 346560ix1 | \([0, 1, 0, -2276225, 1449540735]\) | \(-105756712489/12476160\) | \(-153865929017775882240\) | \([2]\) | \(13271040\) | \(2.6094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.ix have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.ix do not have complex multiplication.Modular form 346560.2.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.
