Properties

Label 227136.ck
Number of curves $2$
Conductor $227136$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 227136.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227136.ck1 227136ij1 \([0, -1, 0, -1408, -18734]\) \(1000000/63\) \(19461693888\) \([2]\) \(147456\) \(0.72536\) \(\Gamma_0(N)\)-optimal
227136.ck2 227136ij2 \([0, -1, 0, 1127, -81095]\) \(8000/147\) \(-2906279620608\) \([2]\) \(294912\) \(1.0719\)  

Rank

sage: E.rank()
 

The elliptic curves in class 227136.ck have rank \(1\).

Complex multiplication

The elliptic curves in class 227136.ck do not have complex multiplication.

Modular form 227136.2.a.ck

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 2 q^{11} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.