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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 11550.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.cc1 | 11550bu4 | \([1, 1, 1, -651088, 201925781]\) | \(1953542217204454969/170843779260\) | \(2669434050937500\) | \([4]\) | \(122880\) | \(2.0013\) | |
| 11550.cc2 | 11550bu3 | \([1, 1, 1, -236088, -41994219]\) | \(93137706732176569/5369647977540\) | \(83900749649062500\) | \([2]\) | \(122880\) | \(2.0013\) | |
| 11550.cc3 | 11550bu2 | \([1, 1, 1, -43588, 2665781]\) | \(586145095611769/140040608400\) | \(2188134506250000\) | \([2, 2]\) | \(61440\) | \(1.6548\) | |
| 11550.cc4 | 11550bu1 | \([1, 1, 1, 6412, 265781]\) | \(1865864036231/2993760000\) | \(-46777500000000\) | \([2]\) | \(30720\) | \(1.3082\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.cc do not have complex multiplication.Modular form 11550.2.a.cc
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
