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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 334620.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
334620.y1 | 334620y2 | \([0, 0, 0, -602823, 180096878]\) | \(26894628304/9075\) | \(8174745505555200\) | \([2]\) | \(3538944\) | \(2.0255\) | |
334620.y2 | 334620y1 | \([0, 0, 0, -32448, 3622853]\) | \(-67108864/61875\) | \(-3483556323390000\) | \([2]\) | \(1769472\) | \(1.6789\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 334620.y have rank \(1\).
Complex multiplication
The elliptic curves in class 334620.y do not have complex multiplication.Modular form 334620.2.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.