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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 152592.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.p1 | 152592bt3 | \([0, -1, 0, -8956784, 9565406784]\) | \(803760366578833/65593817586\) | \(6485095620425680625664\) | \([4]\) | \(10616832\) | \(2.9280\) | |
| 152592.p2 | 152592bt2 | \([0, -1, 0, -1882064, -820282176]\) | \(7457162887153/1370924676\) | \(135539871583242829824\) | \([2, 2]\) | \(5308416\) | \(2.5814\) | |
| 152592.p3 | 152592bt1 | \([0, -1, 0, -1789584, -920826432]\) | \(6411014266033/296208\) | \(29285339293089792\) | \([2]\) | \(2654208\) | \(2.2349\) | \(\Gamma_0(N)\)-optimal |
| 152592.p4 | 152592bt4 | \([0, -1, 0, 3712976, -4772618432]\) | \(57258048889007/132611470002\) | \(-13110962206165832245248\) | \([2]\) | \(10616832\) | \(2.9280\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.p have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.p do not have complex multiplication.Modular form 152592.2.a.p
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.
