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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 215600y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.r2 | 215600y1 | \([0, 1, 0, 254392, 21404788]\) | \(704969/484\) | \(-1249993330432000000\) | \([2]\) | \(2752512\) | \(2.1611\) | \(\Gamma_0(N)\)-optimal |
215600.r1 | 215600y2 | \([0, 1, 0, -1117608, 177812788]\) | \(59776471/29282\) | \(75624596491136000000\) | \([2]\) | \(5505024\) | \(2.5077\) |
Rank
sage: E.rank()
The elliptic curves in class 215600y have rank \(1\).
Complex multiplication
The elliptic curves in class 215600y do not have complex multiplication.Modular form 215600.2.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.