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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 16272y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16272.w2 | 16272y1 | \([0, 0, 0, -239187, 45334802]\) | \(-506814405937489/4048994304\) | \(-12090232207835136\) | \([]\) | \(96768\) | \(1.9139\) | \(\Gamma_0(N)\)-optimal |
16272.w1 | 16272y2 | \([0, 0, 0, -1025427, -4435446958]\) | \(-39934705050538129/2823126576537804\) | \(-8429810787516658139136\) | \([]\) | \(677376\) | \(2.8869\) |
Rank
sage: E.rank()
The elliptic curves in class 16272y have rank \(1\).
Complex multiplication
The elliptic curves in class 16272y do not have complex multiplication.Modular form 16272.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.