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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 388080.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ej1 | 388080ej1 | \([0, 0, 0, -21168, -1083537]\) | \(28311552/2695\) | \(99852348713040\) | \([2]\) | \(1548288\) | \(1.4241\) | \(\Gamma_0(N)\)-optimal |
| 388080.ej2 | 388080ej2 | \([0, 0, 0, 25137, -5167638]\) | \(2963088/21175\) | \(-12552866695353600\) | \([2]\) | \(3096576\) | \(1.7707\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.ej do not have complex multiplication.Modular form 388080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
