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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 116160.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116160.y1 | 116160q1 | \([0, -1, 0, -1710496, 858668626]\) | \(4881508724731456/19372019535\) | \(2196397715164424640\) | \([2]\) | \(2580480\) | \(2.3765\) | \(\Gamma_0(N)\)-optimal |
116160.y2 | 116160q2 | \([0, -1, 0, -905241, 1668594105]\) | \(-11305786504384/159153293475\) | \(-1154866248670676889600\) | \([2]\) | \(5160960\) | \(2.7230\) |
Rank
sage: E.rank()
The elliptic curves in class 116160.y have rank \(2\).
Complex multiplication
The elliptic curves in class 116160.y do not have complex multiplication.Modular form 116160.2.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.