Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 16560.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.br1 | 16560ca2 | \([0, 0, 0, -113187, -10151134]\) | \(53706380371489/16171875000\) | \(48288960000000000\) | \([2]\) | \(92160\) | \(1.9066\) | |
16560.br2 | 16560ca1 | \([0, 0, 0, 19293, -1063006]\) | \(265971760991/317400000\) | \(-947751321600000\) | \([2]\) | \(46080\) | \(1.5600\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.br have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.br do not have complex multiplication.Modular form 16560.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.