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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 209484.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.bj1 | 209484bc2 | \([0, 0, 0, -6152799, 5874154598]\) | \(932410994128/29403\) | \(812318143762084608\) | \([2]\) | \(5406720\) | \(2.5324\) | |
| 209484.bj2 | 209484bc1 | \([0, 0, 0, -368184, 99951905]\) | \(-3196715008/649539\) | \(-1121552891671514544\) | \([2]\) | \(2703360\) | \(2.1858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 209484.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 209484.bj do not have complex multiplication.Modular form 209484.2.a.bj
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.
