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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 9792y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9792.by2 | 9792y1 | \([0, 0, 0, 24, 218]\) | \(32768/459\) | \(-21415104\) | \([]\) | \(2304\) | \(0.087350\) | \(\Gamma_0(N)\)-optimal |
9792.by1 | 9792y2 | \([0, 0, 0, -2136, 38018]\) | \(-23100424192/14739\) | \(-687662784\) | \([]\) | \(6912\) | \(0.63666\) |
Rank
sage: E.rank()
The elliptic curves in class 9792y have rank \(1\).
Complex multiplication
The elliptic curves in class 9792y do not have complex multiplication.Modular form 9792.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.