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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 162240.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.d1 | 162240hp4 | \([0, -1, 0, -146241, -21462975]\) | \(546718898/405\) | \(256227101245440\) | \([2]\) | \(983040\) | \(1.6985\) | |
| 162240.d2 | 162240hp3 | \([0, -1, 0, -92161, 10671361]\) | \(136835858/1875\) | \(1186236579840000\) | \([2]\) | \(983040\) | \(1.6985\) | |
| 162240.d3 | 162240hp2 | \([0, -1, 0, -11041, -182495]\) | \(470596/225\) | \(71174194790400\) | \([2, 2]\) | \(491520\) | \(1.3519\) | |
| 162240.d4 | 162240hp1 | \([0, -1, 0, 2479, -22959]\) | \(21296/15\) | \(-1186236579840\) | \([2]\) | \(245760\) | \(1.0053\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.d have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.d do not have complex multiplication.Modular form 162240.2.a.d
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.
