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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 560.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 560.d1 | 560d4 | \([0, 0, 0, -4283, 107882]\) | \(2121328796049/120050\) | \(491724800\) | \([4]\) | \(384\) | \(0.73213\) | |
| 560.d2 | 560d3 | \([0, 0, 0, -1403, -18902]\) | \(74565301329/5468750\) | \(22400000000\) | \([2]\) | \(384\) | \(0.73213\) | |
| 560.d3 | 560d2 | \([0, 0, 0, -283, 1482]\) | \(611960049/122500\) | \(501760000\) | \([2, 2]\) | \(192\) | \(0.38556\) | |
| 560.d4 | 560d1 | \([0, 0, 0, 37, 138]\) | \(1367631/2800\) | \(-11468800\) | \([2]\) | \(96\) | \(0.038988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 560.d have rank \(1\).
Complex multiplication
The elliptic curves in class 560.d do not have complex multiplication.Modular form 560.2.a.d
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.
