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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 160080cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.s4 | 160080cb1 | \([0, -1, 0, -14536, 138736]\) | \(82933192515529/46103040000\) | \(188838051840000\) | \([2]\) | \(552960\) | \(1.4297\) | \(\Gamma_0(N)\)-optimal |
| 160080.s2 | 160080cb2 | \([0, -1, 0, -142536, -20546064]\) | \(78188073407427529/518918529600\) | \(2125490297241600\) | \([2, 2]\) | \(1105920\) | \(1.7763\) | |
| 160080.s3 | 160080cb3 | \([0, -1, 0, -56136, -45291024]\) | \(-4776347226041929/213760320106680\) | \(-875562271156961280\) | \([2]\) | \(2211840\) | \(2.1229\) | |
| 160080.s1 | 160080cb4 | \([0, -1, 0, -2276936, -1321676304]\) | \(318725217291145165129/14178845880\) | \(58076552724480\) | \([2]\) | \(2211840\) | \(2.1229\) |
Rank
sage: E.rank()
The elliptic curves in class 160080cb have rank \(0\).
Complex multiplication
The elliptic curves in class 160080cb do not have complex multiplication.Modular form 160080.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
