Properties

Label 194145j
Number of curves 4
Conductor 194145
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("194145.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 194145j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
194145.d3 194145j1 [1, 1, 1, -4661, -117982] [2] 322560 \(\Gamma_0(N)\)-optimal
194145.d2 194145j2 [1, 1, 1, -13906, 481094] [2, 2] 645120  
194145.d1 194145j3 [1, 1, 1, -208051, 36436748] [2] 1290240  
194145.d4 194145j4 [1, 1, 1, 32319, 3051204] [2] 1290240  

Rank

sage: E.rank()
 

The elliptic curves in class 194145j have rank \(0\).

Modular form 194145.2.a.d

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 Cremona 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 Cremona labels.