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SageMath
E = EllipticCurve("oq1")
E.isogeny_class()
Elliptic curves in class 388080oq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.oq2 | 388080oq1 | \([0, 0, 0, -63082992, -225841753424]\) | \(-79028701534867456/16987307596875\) | \(-5967607721237710732800000\) | \([]\) | \(92160000\) | \(3.4752\) | \(\Gamma_0(N)\)-optimal |
388080.oq1 | 388080oq2 | \([0, 0, 0, -189032592, 18912291835696]\) | \(-2126464142970105856/438611057788643355\) | \(-154083201246162036370538311680\) | \([]\) | \(460800000\) | \(4.2799\) |
Rank
sage: E.rank()
The elliptic curves in class 388080oq have rank \(0\).
Complex multiplication
The elliptic curves in class 388080oq do not have complex multiplication.Modular form 388080.2.a.oq
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.