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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 96600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.k1 | 96600bl4 | \([0, -1, 0, -60408, 5638812]\) | \(1523681836996/29383305\) | \(470132880000000\) | \([2]\) | \(442368\) | \(1.6082\) | |
| 96600.k2 | 96600bl2 | \([0, -1, 0, -7908, -136188]\) | \(13674725584/5832225\) | \(23328900000000\) | \([2, 2]\) | \(221184\) | \(1.2616\) | |
| 96600.k3 | 96600bl1 | \([0, -1, 0, -6783, -212688]\) | \(138074404864/65205\) | \(16301250000\) | \([2]\) | \(110592\) | \(0.91506\) | \(\Gamma_0(N)\)-optimal |
| 96600.k4 | 96600bl3 | \([0, -1, 0, 26592, -1033188]\) | \(129969187484/103543125\) | \(-1656690000000000\) | \([2]\) | \(442368\) | \(1.6082\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.k have rank \(2\).
Complex multiplication
The elliptic curves in class 96600.k do not have complex multiplication.Modular form 96600.2.a.k
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.
