Properties

Label 227430fz
Number of curves $4$
Conductor $227430$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("227430.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.z4 227430fz1 [1, -1, 0, 9760470, 5089608820] [2] 22394880 \(\Gamma_0(N)\)-optimal
227430.z3 227430fz2 [1, -1, 0, -42916650, 42585182836] [2] 44789760  
227430.z2 227430fz3 [1, -1, 0, -177035370, 928235782196] [2] 67184640  
227430.z1 227430fz4 [1, -1, 0, -2851222290, 58600285736300] [2] 134369280  

Rank

sage: E.rank()
 

The elliptic curves in class 227430fz have rank \(1\).

Modular form 227430.2.a.z

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

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 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.