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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 338130.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.ct1 | 338130ct3 | \([1, -1, 1, -800284838, 8713680460161]\) | \(3221338935539503699129/200350631681460\) | \(3525427376179118715869460\) | \([2]\) | \(117964800\) | \(3.7695\) | |
| 338130.ct2 | 338130ct4 | \([1, -1, 1, -267912158, -1582882592223]\) | \(120859257477573578809/8424459021127500\) | \(148239205503490229515627500\) | \([2]\) | \(117964800\) | \(3.7695\) | |
| 338130.ct3 | 338130ct2 | \([1, -1, 1, -53017538, 118910882481]\) | \(936615448738871929/194959225328400\) | \(3430558638338535138848400\) | \([2, 2]\) | \(58982400\) | \(3.4229\) | |
| 338130.ct4 | 338130ct1 | \([1, -1, 1, 7117582, 11196855537]\) | \(2266209994236551/4390344840960\) | \(-77253771367167733128960\) | \([2]\) | \(29491200\) | \(3.0763\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.ct do not have complex multiplication.Modular form 338130.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
