Properties

Label 1600.n
Number of curves $4$
Conductor $1600$
CM \(\Q(\sqrt{-1}) \)
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality CM discriminant
1600.n1 1600o3 [0, 0, 0, -1100, -14000] [2] 512   -16
1600.n2 1600o4 [0, 0, 0, -1100, 14000] [2] 512   -16
1600.n3 1600o2 [0, 0, 0, -100, 0] [2, 2] 256   -4
1600.n4 1600o1 [0, 0, 0, 25, 0] [2] 128 \(\Gamma_0(N)\)-optimal -4

Rank

sage: E.rank()
 

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

Complex multiplication

Each elliptic curve in class 1600.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 1600.2.a.n

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

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.