Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 1600.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1600.w1 1600r3 \([0, -1, 0, -4133, 103637]\) \(488095744/125\) \(2000000000\) \([2]\) \(1152\) \(0.77065\)  
1600.w2 1600r4 \([0, -1, 0, -3633, 129137]\) \(-20720464/15625\) \(-4000000000000\) \([2]\) \(2304\) \(1.1172\)  
1600.w3 1600r1 \([0, -1, 0, -133, -363]\) \(16384/5\) \(80000000\) \([2]\) \(384\) \(0.22134\) \(\Gamma_0(N)\)-optimal
1600.w4 1600r2 \([0, -1, 0, 367, -2863]\) \(21296/25\) \(-6400000000\) \([2]\) \(768\) \(0.56792\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1600.w do not have complex multiplication.

Modular form 1600.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.