↑

Properties

Label 155526.br
Number of curves $2$
Conductor $155526$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 155526.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.br1 155526bc2 \([1, 1, 1, -700407, -1030044093]\) \(-2181825073/25039686\) \(-436098039886091682246\) \([]\) \(9123840\) \(2.6423\)  
155526.br2 155526bc1 \([1, 1, 1, 77223, 36553215]\) \(2924207/34776\) \(-605668355229323736\) \([]\) \(3041280\) \(2.0930\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 155526.br have rank \(0\).

Complex multiplication

The elliptic curves in class 155526.br do not have complex multiplication.

Modular form 155526.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{8} + q^{9} - 3 q^{10} - q^{12} - 5 q^{13} + 3 q^{15} + q^{16} + q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.