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Properties

Label 227430.u
Number of curves $2$
Conductor $227430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 227430.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227430.u1 227430fx2 \([1, -1, 0, -4200, 105686]\) \(1153270683/1750\) \(12434735250\) \([]\) \(279936\) \(0.83696\)  
227430.u2 227430fx1 \([1, -1, 0, -210, -980]\) \(105359427/13720\) \(133728840\) \([]\) \(93312\) \(0.28766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 227430.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 3 q^{11} - 2 q^{13} - q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.