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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 296240.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296240.bi1 | 296240bi1 | \([0, 0, 0, -24863, 1387038]\) | \(44851536/4025\) | \(152536180025600\) | \([2]\) | \(675840\) | \(1.4612\) | \(\Gamma_0(N)\)-optimal |
| 296240.bi2 | 296240bi2 | \([0, 0, 0, 28037, 6497178]\) | \(16078716/129605\) | \(-19646659987297280\) | \([2]\) | \(1351680\) | \(1.8078\) |
Rank
sage: E.rank()
The elliptic curves in class 296240.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 296240.bi do not have complex multiplication.Modular form 296240.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
