Properties

Label 152592.bu
Number of curves $2$
Conductor $152592$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 152592.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152592.bu1 152592f2 \([0, 1, 0, -841664, -297471564]\) \(666940371553/37026\) \(3660667411636224\) \([2]\) \(1327104\) \(2.0517\)  
152592.bu2 152592f1 \([0, 1, 0, -55584, -4106508]\) \(192100033/38148\) \(3771596727140352\) \([2]\) \(663552\) \(1.7052\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 152592.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 152592.bu do not have complex multiplication.

Modular form 152592.2.a.bu

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - q^{11} + 4 q^{13} - 2 q^{15} - 2 q^{19} + O(q^{20})\) 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.