Properties

Label 51600bx
Number of curves $2$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
51600.d2 51600bx1 [0, -1, 0, -4102408, 3317827312] [2] 2903040 \(\Gamma_0(N)\)-optimal
51600.d1 51600bx2 [0, -1, 0, -66310408, 207857731312] [2] 5806080  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.bx

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.