Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.bp1 51600i1 \([0, -1, 0, -8008, 224512]\) \(3550014724/725625\) \(11610000000000\) \([2]\) \(110592\) \(1.2224\) \(\Gamma_0(N)\)-optimal
51600.bp2 51600i2 \([0, -1, 0, 16992, 1324512]\) \(16954370638/33698025\) \(-1078336800000000\) \([2]\) \(221184\) \(1.5690\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{7} + q^{9} + 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.