Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("227430.ei1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.ei2 227430cv1 [1, -1, 1, -37973, -2835063] [2] 684288 \(\Gamma_0(N)\)-optimal
227430.ei3 227430cv2 [1, -1, 1, -27143, -4494219] [2] 1368576  
227430.ei1 227430cv3 [1, -1, 1, -151688, 19963531] [2] 2052864  
227430.ei4 227430cv4 [1, -1, 1, 238192, 105425227] [2] 4105728  

Rank

sage: E.rank()
 

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

Modular form 227430.2.a.ei

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 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.