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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5775.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5775.v1 | 5775u5 | \([1, 0, 1, -331251, -73404977]\) | \(257260669489908001/14267882475\) | \(222935663671875\) | \([2]\) | \(49152\) | \(1.8186\) | |
| 5775.v2 | 5775u3 | \([1, 0, 1, -21876, -1011227]\) | \(74093292126001/14707625625\) | \(229806650390625\) | \([2, 2]\) | \(24576\) | \(1.4720\) | |
| 5775.v3 | 5775u2 | \([1, 0, 1, -6751, 198773]\) | \(2177286259681/161417025\) | \(2522141015625\) | \([2, 2]\) | \(12288\) | \(1.1254\) | |
| 5775.v4 | 5775u1 | \([1, 0, 1, -6626, 207023]\) | \(2058561081361/12705\) | \(198515625\) | \([2]\) | \(6144\) | \(0.77886\) | \(\Gamma_0(N)\)-optimal |
| 5775.v5 | 5775u4 | \([1, 0, 1, 6374, 881273]\) | \(1833318007919/22507682505\) | \(-351682539140625\) | \([2]\) | \(24576\) | \(1.4720\) | |
| 5775.v6 | 5775u6 | \([1, 0, 1, 45499, -5996977]\) | \(666688497209279/1381398046875\) | \(-21584344482421875\) | \([2]\) | \(49152\) | \(1.8186\) |
Rank
sage: E.rank()
The elliptic curves in class 5775.v have rank \(0\).
Complex multiplication
The elliptic curves in class 5775.v do not have complex multiplication.Modular form 5775.2.a.v
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
