Properties

Label 212160.b
Number of curves 4
Conductor 212160
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("212160.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 212160.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.b1 212160de4 [0, -1, 0, -4903681, -4170818399] [2] 8847360  
212160.b2 212160de3 [0, -1, 0, -4110081, 3191910561] [2] 8847360  
212160.b3 212160de2 [0, -1, 0, -410881, -16775519] [2, 2] 4423680  
212160.b4 212160de1 [0, -1, 0, 101119, -2132319] [2] 2211840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 212160.b have rank \(0\).

Modular form 212160.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - 4q^{7} + q^{9} - 4q^{11} - q^{13} + q^{15} - q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.