Properties

Label 51520.be
Number of curves $2$
Conductor $51520$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 51520.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51520.be1 51520y1 \([0, 0, 0, -10412, -408784]\) \(476196576129/197225\) \(51701350400\) \([2]\) \(73728\) \(1.0177\) \(\Gamma_0(N)\)-optimal
51520.be2 51520y2 \([0, 0, 0, -8812, -538704]\) \(-288673724529/311181605\) \(-81574390661120\) \([2]\) \(147456\) \(1.3643\)  

Rank

sage: E.rank()
 

The elliptic curves in class 51520.be have rank \(1\).

Complex multiplication

The elliptic curves in class 51520.be do not have complex multiplication.

Modular form 51520.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 3 q^{9} - 2 q^{11} - 4 q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) Copy content 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.