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Properties

Label 157170.bw
Number of curves $2$
Conductor $157170$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 157170.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157170.bw1 157170bq2 \([1, 1, 1, -6327786, 5712738039]\) \(5805223604235668521/435937500000000\) \(2104187048437500000000\) \([2]\) \(11612160\) \(2.8369\)  
157170.bw2 157170bq1 \([1, 1, 1, 378134, 396284663]\) \(1238798620042199/14760960000000\) \(-71248334576640000000\) \([2]\) \(5806080\) \(2.4903\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 157170.bw have rank \(0\).

Complex multiplication

The elliptic curves in class 157170.bw do not have complex multiplication.

Modular form 157170.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - 2 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.