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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 364650.ge
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.ge1 | 364650ge2 | \([1, 0, 0, -226133, -154143]\) | \(10230707123604316133/5920484839416576\) | \(740060604927072000\) | \([2]\) | \(5505024\) | \(2.1183\) | |
364650.ge2 | 364650ge1 | \([1, 0, 0, -155733, -23597343]\) | \(3341610468915015653/11498140532736\) | \(1437267566592000\) | \([2]\) | \(2752512\) | \(1.7717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.ge have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.ge do not have complex multiplication.Modular form 364650.2.a.ge
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.