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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 21780.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.j1 | 21780e2 | \([0, 0, 0, -2343, -40898]\) | \(5726576/405\) | \(100600600320\) | \([2]\) | \(18432\) | \(0.85848\) | |
| 21780.j2 | 21780e1 | \([0, 0, 0, 132, -2783]\) | \(16384/225\) | \(-3493076400\) | \([2]\) | \(9216\) | \(0.51191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21780.j have rank \(1\).
Complex multiplication
The elliptic curves in class 21780.j do not have complex multiplication.Modular form 21780.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
