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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 443760.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.c1 | 443760c2 | \([0, -1, 0, -52660136, 172103028336]\) | \(-337335507529/72000000\) | \(-3446990520267866112000000\) | \([]\) | \(74898432\) | \(3.4296\) | \(\Gamma_0(N)\)-optimal* |
443760.c2 | 443760c1 | \([0, -1, 0, 4584904, -1372340880]\) | \(222641831/145800\) | \(-6980155803542428876800\) | \([]\) | \(24966144\) | \(2.8803\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760.c have rank \(0\).
Complex multiplication
The elliptic curves in class 443760.c do not have complex multiplication.Modular form 443760.2.a.c
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.