Properties

Label 145794.r
Number of curves 4
Conductor 145794
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("145794.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 145794.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145794.r1 145794w3 [1, 0, 1, -177871, 28748354] [2] 1251936  
145794.r2 145794w4 [1, 0, 1, -89511, 57341650] [2] 2503872  
145794.r3 145794w1 [1, 0, 1, -12196, -489970] [2] 417312 \(\Gamma_0(N)\)-optimal
145794.r4 145794w2 [1, 0, 1, 9894, -2062778] [2] 834624  

Rank

sage: E.rank()
 

The elliptic curves in class 145794.r have rank \(0\).

Modular form 145794.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.