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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9240.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.d1 | 9240a3 | \([0, -1, 0, -29576, -1947924]\) | \(1397097631688978/433125\) | \(887040000\) | \([2]\) | \(16384\) | \(1.0794\) | |
| 9240.d2 | 9240a2 | \([0, -1, 0, -1856, -29700]\) | \(690862540036/12006225\) | \(12294374400\) | \([2, 2]\) | \(8192\) | \(0.73285\) | |
| 9240.d3 | 9240a1 | \([0, -1, 0, -236, 756]\) | \(5702413264/2525985\) | \(646652160\) | \([2]\) | \(4096\) | \(0.38628\) | \(\Gamma_0(N)\)-optimal |
| 9240.d4 | 9240a4 | \([0, -1, 0, -56, -86580]\) | \(-9653618/1581886845\) | \(-3239704258560\) | \([2]\) | \(16384\) | \(1.0794\) |
Rank
sage: E.rank()
The elliptic curves in class 9240.d have rank \(0\).
Complex multiplication
The elliptic curves in class 9240.d do not have complex multiplication.Modular form 9240.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
