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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 54390.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54390.n1 | 54390k4 | \([1, 1, 0, -15702467, 4924052421]\) | \(3639478711331685826729/2016912141902025000\) | \(237287696582631339225000\) | \([2]\) | \(6635520\) | \(3.1757\) | |
| 54390.n2 | 54390k2 | \([1, 1, 0, -9577467, -11345172579]\) | \(825824067562227826729/5613755625000000\) | \(660452735525625000000\) | \([2, 2]\) | \(3317760\) | \(2.8292\) | |
| 54390.n3 | 54390k1 | \([1, 1, 0, -9561787, -11384363171]\) | \(821774646379511057449/38361600000\) | \(4513203878400000\) | \([2]\) | \(1658880\) | \(2.4826\) | \(\Gamma_0(N)\)-optimal |
| 54390.n4 | 54390k3 | \([1, 1, 0, -3703347, -25105886091]\) | \(-47744008200656797609/2286529541015625000\) | \(-269007913970947265625000\) | \([2]\) | \(6635520\) | \(3.1757\) |
Rank
sage: E.rank()
The elliptic curves in class 54390.n have rank \(1\).
Complex multiplication
The elliptic curves in class 54390.n do not have complex multiplication.Modular form 54390.2.a.n
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.
