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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 229320.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.n1 | 229320dq3 | \([0, 0, 0, -596239203, 5603751974702]\) | \(266912903848829942596/152163375\) | \(13363673530386816000\) | \([2]\) | \(33030144\) | \(3.4309\) | |
| 229320.n2 | 229320dq2 | \([0, 0, 0, -37271703, 87525304202]\) | \(260798860029250384/196803140625\) | \(4321034744838084000000\) | \([2, 2]\) | \(16515072\) | \(3.0843\) | |
| 229320.n3 | 229320dq4 | \([0, 0, 0, -29554203, 124811633702]\) | \(-32506165579682596/57814914850875\) | \(-5077566446289758418816000\) | \([2]\) | \(33030144\) | \(3.4309\) | |
| 229320.n4 | 229320dq1 | \([0, 0, 0, -2818578, 751663577]\) | \(1804588288006144/866455078125\) | \(1188999857144531250000\) | \([2]\) | \(8257536\) | \(2.7377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.n have rank \(0\).
Complex multiplication
The elliptic curves in class 229320.n do not have complex multiplication.Modular form 229320.2.a.n
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.
