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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 82800.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82800.bi1 | 82800ek2 | \([0, 0, 0, -113475, 14701250]\) | \(3463512697/3174\) | \(148086144000000\) | \([2]\) | \(393216\) | \(1.6426\) | |
| 82800.bi2 | 82800ek1 | \([0, 0, 0, -5475, 337250]\) | \(-389017/828\) | \(-38631168000000\) | \([2]\) | \(196608\) | \(1.2960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82800.bi have rank \(2\).
Complex multiplication
The elliptic curves in class 82800.bi do not have complex multiplication.Modular form 82800.2.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.
