Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("1600.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1600.c1 1600g3 [0, 1, 0, -4133, -103637] [2] 1152  
1600.c2 1600g4 [0, 1, 0, -3633, -129137] [2] 2304  
1600.c3 1600g1 [0, 1, 0, -133, 363] [2] 384 \(\Gamma_0(N)\)-optimal
1600.c4 1600g2 [0, 1, 0, 367, 2863] [2] 768  

Rank

sage: E.rank()
 

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

Modular form 1600.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 2q^{7} + q^{9} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.