Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1600.c1 1600g3 \([0, 1, 0, -4133, -103637]\) \(488095744/125\) \(2000000000\) \([2]\) \(1152\) \(0.77065\)  
1600.c2 1600g4 \([0, 1, 0, -3633, -129137]\) \(-20720464/15625\) \(-4000000000000\) \([2]\) \(2304\) \(1.1172\)  
1600.c3 1600g1 \([0, 1, 0, -133, 363]\) \(16384/5\) \(80000000\) \([2]\) \(384\) \(0.22134\) \(\Gamma_0(N)\)-optimal
1600.c4 1600g2 \([0, 1, 0, 367, 2863]\) \(21296/25\) \(-6400000000\) \([2]\) \(768\) \(0.56792\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1600.2.a.c

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