Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.cf1 227430em3 [1, -1, 0, -1213569, 514873503] [2] 3686400  
227430.cf2 227430em2 [1, -1, 0, -76419, 7932033] [2, 2] 1843200  
227430.cf3 227430em1 [1, -1, 0, -11439, -294435] [2] 921600 \(\Gamma_0(N)\)-optimal
227430.cf4 227430em4 [1, -1, 0, 21051, 26704755] [2] 3686400  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 227430.cf do not have complex multiplication.

Modular form 227430.2.a.cf

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{14} + q^{16} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.