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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5610.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5610.n1 | 5610m3 | \([1, 0, 1, -9989, 383402]\) | \(110211585818155849/993794670\) | \(993794670\) | \([2]\) | \(9216\) | \(0.89162\) | |
| 5610.n2 | 5610m2 | \([1, 0, 1, -639, 5662]\) | \(28790481449449/2549240100\) | \(2549240100\) | \([2, 2]\) | \(4608\) | \(0.54505\) | |
| 5610.n3 | 5610m1 | \([1, 0, 1, -139, -538]\) | \(293946977449/50490000\) | \(50490000\) | \([2]\) | \(2304\) | \(0.19847\) | \(\Gamma_0(N)\)-optimal |
| 5610.n4 | 5610m4 | \([1, 0, 1, 711, 26722]\) | \(39829997144951/330164359470\) | \(-330164359470\) | \([2]\) | \(9216\) | \(0.89162\) |
Rank
sage: E.rank()
The elliptic curves in class 5610.n have rank \(1\).
Complex multiplication
The elliptic curves in class 5610.n do not have complex multiplication.Modular form 5610.2.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.
