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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 344760.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.cc1 | 344760cc4 | \([0, 1, 0, -15250616, -17094052416]\) | \(79364416584061444/20404090514925\) | \(100850327279876735308800\) | \([2]\) | \(33030144\) | \(3.1233\) | |
| 344760.cc2 | 344760cc2 | \([0, 1, 0, -5364116, 4561337184]\) | \(13813960087661776/714574355625\) | \(882973166310387360000\) | \([2, 2]\) | \(16515072\) | \(2.7768\) | |
| 344760.cc3 | 344760cc1 | \([0, 1, 0, -5295671, 4688836530]\) | \(212670222886967296/616241925\) | \(47591713116277200\) | \([4]\) | \(8257536\) | \(2.4302\) | \(\Gamma_0(N)\)-optimal |
| 344760.cc4 | 344760cc3 | \([0, 1, 0, 3427264, 18057863760]\) | \(900753985478876/29018422265625\) | \(-143427974919699600000000\) | \([2]\) | \(33030144\) | \(3.1233\) |
Rank
sage: E.rank()
The elliptic curves in class 344760.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.cc do not have complex multiplication.Modular form 344760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
