Properties

Label 176505.r
Number of curves 4
Conductor 176505
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("176505.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176505.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176505.r1 176505s4 [1, 1, 0, -189147, -31739316] [2] 1105920  
176505.r2 176505s2 [1, 1, 0, -12642, -427329] [2, 2] 552960  
176505.r3 176505s1 [1, 1, 0, -4237, 98824] [2] 276480 \(\Gamma_0(N)\)-optimal
176505.r4 176505s3 [1, 1, 0, 29383, -2621034] [2] 1105920  

Rank

sage: E.rank()
 

The elliptic curves in class 176505.r have rank \(0\).

Modular form 176505.2.a.r

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - q^{7} - 3q^{8} + q^{9} + q^{10} + q^{12} + 6q^{13} - q^{14} - q^{15} - q^{16} - 2q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.