Properties

Label 159120bd
Number of curves 4
Conductor 159120
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("159120.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 159120bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159120.b4 159120bd1 [0, 0, 0, 227517, 7082818] [2] 2211840 \(\Gamma_0(N)\)-optimal
159120.b3 159120bd2 [0, 0, 0, -924483, 57079618] [2, 2] 4423680  
159120.b1 159120bd3 [0, 0, 0, -11033283, 14082028738] [2] 8847360  
159120.b2 159120bd4 [0, 0, 0, -9247683, -10768074302] [2] 8847360  

Rank

sage: E.rank()
 

The elliptic curves in class 159120bd have rank \(1\).

Modular form 159120.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 4q^{11} + q^{13} + q^{17} - 8q^{19} + O(q^{20}) \)

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.