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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 8880.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8880.a1 | 8880l3 | \([0, -1, 0, -5127336, 921703536]\) | \(3639478711331685826729/2016912141902025000\) | \(8261272133230694400000\) | \([2]\) | \(552960\) | \(2.8959\) | |
| 8880.a2 | 8880l2 | \([0, -1, 0, -3127336, -2115096464]\) | \(825824067562227826729/5613755625000000\) | \(22993943040000000000\) | \([2, 2]\) | \(276480\) | \(2.5494\) | |
| 8880.a3 | 8880l1 | \([0, -1, 0, -3122216, -2122411920]\) | \(821774646379511057449/38361600000\) | \(157129113600000\) | \([2]\) | \(138240\) | \(2.2028\) | \(\Gamma_0(N)\)-optimal |
| 8880.a4 | 8880l4 | \([0, -1, 0, -1209256, -4683789200]\) | \(-47744008200656797609/2286529541015625000\) | \(-9365625000000000000000\) | \([2]\) | \(552960\) | \(2.8959\) |
Rank
sage: E.rank()
The elliptic curves in class 8880.a have rank \(0\).
Complex multiplication
The elliptic curves in class 8880.a do not have complex multiplication.Modular form 8880.2.a.a
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.
