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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 62400ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.br2 | 62400ey1 | \([0, -1, 0, -33, -48063]\) | \(-4/975\) | \(-998400000000\) | \([2]\) | \(73728\) | \(0.98134\) | \(\Gamma_0(N)\)-optimal |
62400.br1 | 62400ey2 | \([0, -1, 0, -20033, -1068063]\) | \(434163602/7605\) | \(15575040000000\) | \([2]\) | \(147456\) | \(1.3279\) |
Rank
sage: E.rank()
The elliptic curves in class 62400ey have rank \(1\).
Complex multiplication
The elliptic curves in class 62400ey do not have complex multiplication.Modular form 62400.2.a.ey
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.