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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 44400.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.cq1 | 44400l1 | \([0, 1, 0, -283, 1688]\) | \(10061824/333\) | \(83250000\) | \([2]\) | \(10240\) | \(0.29286\) | \(\Gamma_0(N)\)-optimal |
44400.cq2 | 44400l2 | \([0, 1, 0, 92, 6188]\) | \(21296/4107\) | \(-16428000000\) | \([2]\) | \(20480\) | \(0.63943\) |
Rank
sage: E.rank()
The elliptic curves in class 44400.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 44400.cq do not have complex multiplication.Modular form 44400.2.a.cq
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.