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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 38640.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.j1 | 38640b4 | \([0, -1, 0, -220816, -39865184]\) | \(581416486276209698/12425175\) | \(25446758400\) | \([2]\) | \(131072\) | \(1.5244\) | |
| 38640.j2 | 38640b2 | \([0, -1, 0, -13816, -617984]\) | \(284840777767396/1312250625\) | \(1343744640000\) | \([2, 2]\) | \(65536\) | \(1.1778\) | |
| 38640.j3 | 38640b3 | \([0, -1, 0, -6816, -1250784]\) | \(-17101973157698/321306440175\) | \(-658035589478400\) | \([2]\) | \(131072\) | \(1.5244\) | |
| 38640.j4 | 38640b1 | \([0, -1, 0, -1316, 2016]\) | \(985329269584/566015625\) | \(144900000000\) | \([2]\) | \(32768\) | \(0.83124\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.j have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.j do not have complex multiplication.Modular form 38640.2.a.j
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.
