Properties

Label 162.d
Number of curves 2
Conductor 162
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("162.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162.d1 162d2 [1, -1, 1, -56, -161] [] 36  
162.d2 162d1 [1, -1, 1, 4, -1] [3] 12 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 162.d have rank \(0\).

Modular form 162.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 3q^{5} - 4q^{7} + q^{8} + 3q^{10} - q^{13} - 4q^{14} + q^{16} + 3q^{17} - 4q^{19} + O(q^{20}) \)

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.