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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 379050.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.y1 | 379050y1 | \([1, 1, 0, -164775, -25797375]\) | \(4616586342451/3307500\) | \(354470976562500\) | \([2]\) | \(3317760\) | \(1.7271\) | \(\Gamma_0(N)\)-optimal |
379050.y2 | 379050y2 | \([1, 1, 0, -131525, -36470625]\) | \(-2347864201171/3986718750\) | \(-427264123535156250\) | \([2]\) | \(6635520\) | \(2.0737\) |
Rank
sage: E.rank()
The elliptic curves in class 379050.y have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.y do not have complex multiplication.Modular form 379050.2.a.y
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.