Properties

Label 463680.ck
Number of curves $2$
Conductor $463680$
CM no
Rank $1$
Graph

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

Elliptic curves in class 463680.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ck1 463680ck1 \([0, 0, 0, -13548, 334672]\) \(1439069689/579600\) \(110763284889600\) \([2]\) \(1179648\) \(1.3928\) \(\Gamma_0(N)\)-optimal
463680.ck2 463680ck2 \([0, 0, 0, 44052, 2431312]\) \(49471280711/41992020\) \(-8024799990251520\) \([2]\) \(2359296\) \(1.7394\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680.ck have rank \(1\).

Complex multiplication

The elliptic curves in class 463680.ck do not have complex multiplication.

Modular form 463680.2.a.ck

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + 2q^{11} - 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.