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Properties

Label 227430fy
Number of curves $2$
Conductor $227430$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("fy1")
 
E.isogeny_class()
 

Elliptic curves in class 227430fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227430.x2 227430fy1 \([1, -1, 0, -3684975, 1872198125]\) \(5976054062523/1824760000\) \(1689735197216301480000\) \([2]\) \(13271040\) \(2.7781\) \(\Gamma_0(N)\)-optimal
227430.x1 227430fy2 \([1, -1, 0, -22789095, -40428144379]\) \(1413487789441083/55278125000\) \(51187769048325459375000\) \([2]\) \(26542080\) \(3.1247\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 227430.2.a.fy

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.