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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 176400ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.qh2 | 176400ch1 | \([0, 0, 0, 790125, -226808750]\) | \(397535/392\) | \(-53792511091200000000\) | \([]\) | \(4147200\) | \(2.4730\) | \(\Gamma_0(N)\)-optimal |
176400.qh1 | 176400ch2 | \([0, 0, 0, -8029875, 12306411250]\) | \(-417267265/235298\) | \(-32288954782492800000000\) | \([]\) | \(12441600\) | \(3.0223\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ch have rank \(1\).
Complex multiplication
The elliptic curves in class 176400ch do not have complex multiplication.Modular form 176400.2.a.ch
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.