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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 95550.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.y1 | 95550q1 | \([1, 1, 0, -56375, 4334625]\) | \(10779215329/1774500\) | \(3262002351562500\) | \([2]\) | \(663552\) | \(1.6983\) | \(\Gamma_0(N)\)-optimal |
95550.y2 | 95550q2 | \([1, 1, 0, 102875, 24559375]\) | \(65499561791/179156250\) | \(-329336775878906250\) | \([2]\) | \(1327104\) | \(2.0449\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.y have rank \(2\).
Complex multiplication
The elliptic curves in class 95550.y do not have complex multiplication.Modular form 95550.2.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.