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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 89280.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
89280.cn1 | 89280bh4 | \([0, 0, 0, -871788, 299809712]\) | \(383432500775449/18701300250\) | \(3573874132844544000\) | \([2]\) | \(1769472\) | \(2.3196\) | |
89280.cn2 | 89280bh2 | \([0, 0, 0, -151788, -16702288]\) | \(2023804595449/540562500\) | \(103303102464000000\) | \([2, 2]\) | \(884736\) | \(1.9730\) | |
89280.cn3 | 89280bh1 | \([0, 0, 0, -140268, -20218192]\) | \(1597099875769/186000\) | \(35545153536000\) | \([2]\) | \(442368\) | \(1.6265\) | \(\Gamma_0(N)\)-optimal |
89280.cn4 | 89280bh3 | \([0, 0, 0, 383892, -108196432]\) | \(32740359775271/45410156250\) | \(-8678016000000000000\) | \([2]\) | \(1769472\) | \(2.3196\) |
Rank
sage: E.rank()
The elliptic curves in class 89280.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 89280.cn do not have complex multiplication.Modular form 89280.2.a.cn
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.