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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 9900q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9900.h2 | 9900q1 | \([0, 0, 0, 600, 6500]\) | \(8192/11\) | \(-32076000000\) | \([]\) | \(6480\) | \(0.70173\) | \(\Gamma_0(N)\)-optimal |
9900.h1 | 9900q2 | \([0, 0, 0, -17400, 888500]\) | \(-199794688/1331\) | \(-3881196000000\) | \([]\) | \(19440\) | \(1.2510\) |
Rank
sage: E.rank()
The elliptic curves in class 9900q have rank \(0\).
Complex multiplication
The elliptic curves in class 9900q do not have complex multiplication.Modular form 9900.2.a.q
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.