Properties

Label 51600.du
Number of curves $4$
Conductor $51600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("du1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.du1 51600w4 \([0, 1, 0, -6495408, -6373780812]\) \(947094050118111698/20769216075\) \(664614914400000000\) \([2]\) \(1966080\) \(2.5356\)  
51600.du2 51600w2 \([0, 1, 0, -420408, -92230812]\) \(513591322675396/68238500625\) \(1091816010000000000\) \([2, 2]\) \(983040\) \(2.1890\)  
51600.du3 51600w1 \([0, 1, 0, -107908, 12144188]\) \(34739908901584/4081640625\) \(16326562500000000\) \([2]\) \(491520\) \(1.8424\) \(\Gamma_0(N)\)-optimal
51600.du4 51600w3 \([0, 1, 0, 654592, -485680812]\) \(969360123836302/3748293231075\) \(-119945383394400000000\) \([2]\) \(1966080\) \(2.5356\)  

Rank

sage: E.rank()
 

The elliptic curves in class 51600.du have rank \(0\).

Complex multiplication

The elliptic curves in class 51600.du do not have complex multiplication.

Modular form 51600.2.a.du

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.