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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 129360.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.bi1 | 129360dq2 | \([0, -1, 0, -43136, 4206336]\) | \(-902612375329/249562500\) | \(-2454321408000000\) | \([]\) | \(870912\) | \(1.6688\) | |
| 129360.bi2 | 129360dq1 | \([0, -1, 0, 3904, -46080]\) | \(668944031/475200\) | \(-4673352499200\) | \([]\) | \(290304\) | \(1.1195\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.bi do not have complex multiplication.Modular form 129360.2.a.bi
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
