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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2730.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2730.u1 | 2730w5 | \([1, 1, 1, -61165, -5847895]\) | \(25306558948218234961/4478906250\) | \(4478906250\) | \([2]\) | \(8192\) | \(1.2484\) | |
| 2730.u2 | 2730w3 | \([1, 1, 1, -3835, -91963]\) | \(6237734630203441/82168222500\) | \(82168222500\) | \([2, 2]\) | \(4096\) | \(0.90187\) | |
| 2730.u3 | 2730w6 | \([1, 1, 1, -585, -238863]\) | \(-22143063655441/24584858584650\) | \(-24584858584650\) | \([2]\) | \(8192\) | \(1.2484\) | |
| 2730.u4 | 2730w2 | \([1, 1, 1, -455, 1325]\) | \(10418796526321/5038160400\) | \(5038160400\) | \([2, 4]\) | \(2048\) | \(0.55529\) | |
| 2730.u5 | 2730w1 | \([1, 1, 1, -375, 2637]\) | \(5832972054001/4542720\) | \(4542720\) | \([4]\) | \(1024\) | \(0.20872\) | \(\Gamma_0(N)\)-optimal |
| 2730.u6 | 2730w4 | \([1, 1, 1, 1645, 12245]\) | \(492271755328079/342606902820\) | \(-342606902820\) | \([4]\) | \(4096\) | \(0.90187\) |
Rank
sage: E.rank()
The elliptic curves in class 2730.u have rank \(0\).
Complex multiplication
The elliptic curves in class 2730.u do not have complex multiplication.Modular form 2730.2.a.u
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
