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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 166410.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.ct1 | 166410f2 | \([1, -1, 1, -29621327, 72605965079]\) | \(-337335507529/72000000\) | \(-613490256170721288000000\) | \([3]\) | \(24966144\) | \(3.2858\) | |
166410.ct2 | 166410f1 | \([1, -1, 1, 2579008, -578956309]\) | \(222641831/145800\) | \(-1242317768745710608200\) | \([]\) | \(8322048\) | \(2.7364\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 166410.ct do not have complex multiplication.Modular form 166410.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.