Properties

Label 137904.bx
Number of curves $2$
Conductor $137904$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 137904.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137904.bx1 137904e2 \([0, 1, 0, -414444, -102831624]\) \(6371214852688/77571\) \(95851622640384\) \([2]\) \(1161216\) \(1.8312\)  
137904.bx2 137904e1 \([0, 1, 0, -26589, -1523898]\) \(26919436288/2738853\) \(211518724961232\) \([2]\) \(580608\) \(1.4846\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 137904.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 137904.bx do not have complex multiplication.

Modular form 137904.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 4 q^{7} + q^{9} + 2 q^{11} - 2 q^{15} + q^{17} + 2 q^{19} + O(q^{20})\) 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.