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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 44352.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.ej1 | 44352ej4 | \([0, 0, 0, -23182284, 42961797520]\) | \(7209828390823479793/49509306\) | \(9461375716294656\) | \([2]\) | \(1179648\) | \(2.6653\) | |
| 44352.ej2 | 44352ej3 | \([0, 0, 0, -2020044, 93992848]\) | \(4770223741048753/2740574865798\) | \(523732012804798414848\) | \([2]\) | \(1179648\) | \(2.6653\) | |
| 44352.ej3 | 44352ej2 | \([0, 0, 0, -1449804, 670391440]\) | \(1763535241378513/4612311396\) | \(881426434014314496\) | \([2, 2]\) | \(589824\) | \(2.3187\) | |
| 44352.ej4 | 44352ej1 | \([0, 0, 0, -55884, 18594448]\) | \(-100999381393/723148272\) | \(-138195786868457472\) | \([2]\) | \(294912\) | \(1.9721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44352.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 44352.ej do not have complex multiplication.Modular form 44352.2.a.ej
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.
