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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 470925y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
470925.y2 | 470925y1 | \([1, -1, 1, 3820, 89822]\) | \(541343375/625807\) | \(-7128332859375\) | \([2]\) | \(829440\) | \(1.1526\) | \(\Gamma_0(N)\)-optimal* |
470925.y1 | 470925y2 | \([1, -1, 1, -22055, 866072]\) | \(104154702625/32188247\) | \(366644250984375\) | \([2]\) | \(1658880\) | \(1.4992\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 470925y have rank \(1\).
Complex multiplication
The elliptic curves in class 470925y do not have complex multiplication.Modular form 470925.2.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 Cremona 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 Cremona labels.