Properties

Label 418950kk
Number of curves $4$
Conductor $418950$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("418950.kk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 418950kk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
418950.kk3 418950kk1 [1, -1, 1, -342005, 76607997] [2] 4718592 \(\Gamma_0(N)\)-optimal
418950.kk2 418950kk2 [1, -1, 1, -562505, -34083003] [2, 2] 9437184  
418950.kk4 418950kk3 [1, -1, 1, 2193745, -271120503] [2] 18874368  
418950.kk1 418950kk4 [1, -1, 1, -6846755, -6883915503] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 418950kk have rank \(1\).

Modular form 418950.2.a.kk

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + q^{19} + O(q^{20}) \)

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.