Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("227430.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 227430fd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.i3 227430fd1 [1, -1, 0, -42813765, -107800072619] [2] 17694720 \(\Gamma_0(N)\)-optimal
227430.i2 227430fd2 [1, -1, 0, -46972485, -85591676075] [2, 2] 35389440  
227430.i1 227430fd3 [1, -1, 0, -288958005, 1824593621701] [2] 70778880  
227430.i4 227430fd4 [1, -1, 0, 128473515, -574489499675] [2] 70778880  

Rank

sage: E.rank()
 

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

Modular form 227430.2.a.i

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.