Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.cv1 51600db4 \([0, 1, 0, -26549408, -52658476812]\) \(32337636827233520089/3023437500000\) \(193500000000000000000\) \([2]\) \(4423680\) \(2.9304\)  
51600.cv2 51600db3 \([0, 1, 0, -9781408, 11192787188]\) \(1617141066657115609/89723013444000\) \(5742272860416000000000\) \([4]\) \(4423680\) \(2.9304\)  
51600.cv3 51600db2 \([0, 1, 0, -1781408, -695212812]\) \(9768641617435609/2396304000000\) \(153363456000000000000\) \([2, 2]\) \(2211840\) \(2.5839\)  
51600.cv4 51600db1 \([0, 1, 0, 266592, -68524812]\) \(32740359775271/50724864000\) \(-3246391296000000000\) \([2]\) \(1105920\) \(2.2373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4q^{11} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.