Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 90944.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90944.br1 | 90944bq2 | \([0, -1, 0, -1426945, 661007873]\) | \(-10418796526321/82044596\) | \(-2530335699711819776\) | \([]\) | \(1382400\) | \(2.3598\) | |
| 90944.br2 | 90944bq1 | \([0, -1, 0, 15615, -1252607]\) | \(13651919/29696\) | \(-915853725925376\) | \([]\) | \(276480\) | \(1.5551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90944.br have rank \(1\).
Complex multiplication
The elliptic curves in class 90944.br do not have complex multiplication.Modular form 90944.2.a.br
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
