Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bv1 51600bw4 \([0, -1, 0, -2201608, 1258089712]\) \(18440127492397057/1032\) \(66048000000\) \([2]\) \(737280\) \(1.9909\)  
51600.bv2 51600bw2 \([0, -1, 0, -137608, 19689712]\) \(4502751117697/1065024\) \(68161536000000\) \([2, 2]\) \(368640\) \(1.6444\)  
51600.bv3 51600bw3 \([0, -1, 0, -121608, 24425712]\) \(-3107661785857/2215383048\) \(-141784515072000000\) \([2]\) \(737280\) \(1.9909\)  
51600.bv4 51600bw1 \([0, -1, 0, -9608, 233712]\) \(1532808577/528384\) \(33816576000000\) \([2]\) \(184320\) \(1.2978\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.bv

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.