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Properties

Label 158950br
Number of curves $2$
Conductor $158950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 158950br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158950.dh1 158950br1 \([1, 0, 0, -639563, 198693617]\) \(-76711450249/851840\) \(-321271043390000000\) \([]\) \(3386880\) \(2.1741\) \(\Gamma_0(N)\)-optimal
158950.dh2 158950br2 \([1, 0, 0, 2142062, 1030399492]\) \(2882081488391/2883584000\) \(-1087542308864000000000\) \([]\) \(10160640\) \(2.7234\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158950br have rank \(0\).

Complex multiplication

The elliptic curves in class 158950br do not have complex multiplication.

Modular form 158950.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{11} + q^{12} - 2 q^{13} + 5 q^{14} + q^{16} - 2 q^{18} - 7 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.