Properties

Label 1600a
Number of curves 4
Conductor 1600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1600.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1600.o3 1600a1 [0, 0, 0, -200, 1000] [2] 384 \(\Gamma_0(N)\)-optimal
1600.o2 1600a2 [0, 0, 0, -700, -6000] [2, 2] 768  
1600.o1 1600a3 [0, 0, 0, -10700, -426000] [2] 1536  
1600.o4 1600a4 [0, 0, 0, 1300, -34000] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 1600a have rank \(1\).

Modular form 1600.2.a.o

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 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.