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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 15600.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.cy1 | 15600cl3 | \([0, 1, 0, -34611408, -78386440812]\) | \(71647584155243142409/10140000\) | \(648960000000000\) | \([2]\) | \(737280\) | \(2.6951\) | |
| 15600.cy2 | 15600cl4 | \([0, 1, 0, -2483408, -839176812]\) | \(26465989780414729/10571870144160\) | \(676599689226240000000\) | \([4]\) | \(737280\) | \(2.6951\) | |
| 15600.cy3 | 15600cl2 | \([0, 1, 0, -2163408, -1225096812]\) | \(17496824387403529/6580454400\) | \(421149081600000000\) | \([2, 2]\) | \(368640\) | \(2.3486\) | |
| 15600.cy4 | 15600cl1 | \([0, 1, 0, -115408, -24968812]\) | \(-2656166199049/2658140160\) | \(-170120970240000000\) | \([2]\) | \(184320\) | \(2.0020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.cy do not have complex multiplication.Modular form 15600.2.a.cy
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.
