Properties

Label 234416bg
Number of curves $2$
Conductor $234416$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 234416bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234416.bg1 234416bg1 \([0, 0, 0, -27244, 562863]\) \(1188031905792/614810677\) \(1157309781413968\) \([2]\) \(622080\) \(1.5824\) \(\Gamma_0(N)\)-optimal
234416.bg2 234416bg2 \([0, 0, 0, 102361, 4373250]\) \(3938211778608/2553381961\) \(-76903125588400384\) \([2]\) \(1244160\) \(1.9290\)  

Rank

sage: E.rank()
 

The elliptic curves in class 234416bg have rank \(0\).

Complex multiplication

The elliptic curves in class 234416bg do not have complex multiplication.

Modular form 234416.2.a.bg

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 3 q^{9} - 2 q^{11} + q^{13} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.