↑

Properties

Label 28050.bp
Number of curves $2$
Conductor $28050$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 28050.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.bp1 28050bg2 \([1, 0, 1, -27702676, 40002980498]\) \(150476552140919246594353/42832838728685592576\) \(669263105135712384000000\) \([2]\) \(4153344\) \(3.2784\)  
28050.bp2 28050bg1 \([1, 0, 1, -10294676, -12221019502]\) \(7722211175253055152433/340131399900069888\) \(5314553123438592000000\) \([2]\) \(2076672\) \(2.9318\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28050.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 28050.bp do not have complex multiplication.

Modular form 28050.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{11} + q^{12} - 4 q^{13} - 2 q^{14} + q^{16} - q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.