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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 271062o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271062.o3 | 271062o1 | \([1, -1, 0, -147599676, 691888059904]\) | \(-3753503985421/10392624\) | \(-984619108639456715482992\) | \([2]\) | \(68198400\) | \(3.4768\) | \(\Gamma_0(N)\)-optimal |
| 271062.o2 | 271062o2 | \([1, -1, 0, -2363161896, 44217494096692]\) | \(15404978391891661/117612\) | \(11142808842627596574396\) | \([2]\) | \(136396800\) | \(3.8234\) | |
| 271062.o4 | 271062o3 | \([1, -1, 0, 1062753759, -12470122934915]\) | \(1401130594505699/1519867920384\) | \(-143995491130844226232828035072\) | \([2]\) | \(340992000\) | \(4.2816\) | |
| 271062.o1 | 271062o4 | \([1, -1, 0, -5939516961, -116477650847363]\) | \(244587381607181341/79679768374272\) | \(7549029245479685377286193970176\) | \([2]\) | \(681984000\) | \(4.6281\) |
Rank
sage: E.rank()
The elliptic curves in class 271062o have rank \(0\).
Complex multiplication
The elliptic curves in class 271062o do not have complex multiplication.Modular form 271062.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
