Properties

Label 133848.bx
Number of curves $2$
Conductor $133848$
CM no
Rank $0$
Graph

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

Elliptic curves in class 133848.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133848.bx1 133848bp1 \([0, 0, 0, -12192843, 16387225270]\) \(55635379958596/24057\) \(86682028706178048\) \([2]\) \(6322176\) \(2.5925\) \(\Gamma_0(N)\)-optimal
133848.bx2 133848bp2 \([0, 0, 0, -12132003, 16558854910]\) \(-27403349188178/578739249\) \(-4170619129169050601472\) \([2]\) \(12644352\) \(2.9391\)  

Rank

sage: E.rank()
 

The elliptic curves in class 133848.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 133848.bx do not have complex multiplication.

Modular form 133848.2.a.bx

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