Properties

Label 156702.u
Number of curves $2$
Conductor $156702$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 156702.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156702.u1 156702bw1 \([1, 0, 1, -21145, 9165692]\) \(-181356420553/6192965376\) \(-35701212992530176\) \([3]\) \(1935360\) \(1.8565\) \(\Gamma_0(N)\)-optimal
156702.u2 156702bw2 \([1, 0, 1, 189800, -243883930]\) \(131169029575367/4533723856896\) \(-26136015823957917696\) \([]\) \(5806080\) \(2.4058\)  

Rank

sage: E.rank()
 

The elliptic curves in class 156702.u have rank \(0\).

Complex multiplication

The elliptic curves in class 156702.u do not have complex multiplication.

Modular form 156702.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{8} + q^{9} + 3 q^{10} + q^{12} + q^{13} - 3 q^{15} + q^{16} + 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.