Properties

Label 1600.d
Number of curves $2$
Conductor $1600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1600.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1600.d1 1600x2 \([0, 1, 0, -113, -497]\) \(78608\) \(2048000\) \([2]\) \(256\) \(0.019928\)  
1600.d2 1600x1 \([0, 1, 0, -13, 3]\) \(2048\) \(128000\) \([2]\) \(128\) \(-0.32665\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1600.2.a.d

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.