Properties

Label 227430.cu
Number of curves $4$
Conductor $227430$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("227430.cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.cu1 227430fp3 [1, -1, 0, -341754, 76888448] [2] 2052864  
227430.cu2 227430fp4 [1, -1, 0, -244284, 121588190] [2] 4105728  
227430.cu3 227430fp1 [1, -1, 0, -16854, -733772] [2] 684288 \(\Gamma_0(N)\)-optimal
227430.cu4 227430fp2 [1, -1, 0, 26466, -3913460] [2] 1368576  

Rank

sage: E.rank()
 

The elliptic curves in class 227430.cu have rank \(0\).

Modular form 227430.2.a.cu

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - 2q^{13} - q^{14} + q^{16} + O(q^{20}) \)

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.