Properties

Label 222530n
Number of curves 4
Conductor 222530
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("222530.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 222530n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
222530.bw3 222530n1 [1, 1, 1, -16190, 15423355] [2] 2985984 \(\Gamma_0(N)\)-optimal
222530.bw2 222530n2 [1, 1, 1, -1033470, 400362107] [2] 5971968  
222530.bw4 222530n3 [1, 1, 1, 145650, -415588933] [2] 8957952  
222530.bw1 222530n4 [1, 1, 1, -7547530, -7757959925] [2] 17915904  

Rank

sage: E.rank()
 

The elliptic curves in class 222530n have rank \(0\).

Modular form 222530.2.a.bw

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + 2q^{12} - 4q^{13} - q^{14} + 2q^{15} + q^{16} + q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.