Properties

Label 130536bm
Number of curves $2$
Conductor $130536$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 130536bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130536.h1 130536bm1 \([0, 0, 0, -7444962, -7818830775]\) \(33256413948450816/2481997\) \(3405940080378192\) \([2]\) \(3760128\) \(2.4300\) \(\Gamma_0(N)\)-optimal
130536.h2 130536bm2 \([0, 0, 0, -7429527, -7852864950]\) \(-2065624967846736/17960084863\) \(-394333903751763564288\) \([2]\) \(7520256\) \(2.7766\)  

Rank

sage: E.rank()
 

The elliptic curves in class 130536bm have rank \(1\).

Complex multiplication

The elliptic curves in class 130536bm do not have complex multiplication.

Modular form 130536.2.a.bm

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + 4 q^{11} + 4 q^{13} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.