Properties

Label 1600.k
Number of curves 4
Conductor 1600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1600.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1600.k1 1600p3 [0, 0, 0, -10700, 426000] [2] 1536  
1600.k2 1600p2 [0, 0, 0, -700, 6000] [2, 2] 768  
1600.k3 1600p1 [0, 0, 0, -200, -1000] [2] 384 \(\Gamma_0(N)\)-optimal
1600.k4 1600p4 [0, 0, 0, 1300, 34000] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 1600.k have rank \(0\).

Modular form 1600.2.a.k

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.