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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 171600.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 171600.bj1 | 171600eb2 | \([0, -1, 0, -11730408, 15467763312]\) | \(2789222297765780449/677605500\) | \(43366752000000000\) | \([2]\) | \(5308416\) | \(2.5696\) | |
| 171600.bj2 | 171600eb1 | \([0, -1, 0, -730408, 243763312]\) | \(-673350049820449/10617750000\) | \(-679536000000000000\) | \([2]\) | \(2654208\) | \(2.2231\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 171600.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 171600.bj do not have complex multiplication.Modular form 171600.2.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.
