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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 489566.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489566.y1 | 489566y1 | \([1, -1, 0, -26565512, -49778558912]\) | \(9869198625/614656\) | \(129130409635030851229952\) | \([2]\) | \(50135040\) | \(3.1860\) | \(\Gamma_0(N)\)-optimal |
489566.y2 | 489566y2 | \([1, -1, 0, 20992328, -208536140400]\) | \(4869777375/92236816\) | \(-19377632095856817112694672\) | \([2]\) | \(100270080\) | \(3.5326\) |
Rank
sage: E.rank()
The elliptic curves in class 489566.y have rank \(1\).
Complex multiplication
The elliptic curves in class 489566.y do not have complex multiplication.Modular form 489566.2.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.