Properties

Label 58608bq
Number of curves $4$
Conductor $58608$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 58608bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58608.bo4 58608bq1 \([0, 0, 0, -3281259, 1972979098]\) \(1308451928740468777/194033737531392\) \(579381635728936009728\) \([2]\) \(2949120\) \(2.7086\) \(\Gamma_0(N)\)-optimal
58608.bo2 58608bq2 \([0, 0, 0, -50467179, 137991112090]\) \(4760617885089919932457/133756441657344\) \(399394594685762666496\) \([2, 2]\) \(5898240\) \(3.0552\)  
58608.bo3 58608bq3 \([0, 0, 0, -48439659, 149586498970]\) \(-4209586785160189454377/801182513521564416\) \(-2392318166455175001145344\) \([2]\) \(11796480\) \(3.4018\)  
58608.bo1 58608bq4 \([0, 0, 0, -807469419, 8831556236698]\) \(19499096390516434897995817/15393430272\) \(45964536497307648\) \([4]\) \(11796480\) \(3.4018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58608bq have rank \(1\).

Complex multiplication

The elliptic curves in class 58608bq do not have complex multiplication.

Modular form 58608.2.a.bq

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + 4 q^{7} + q^{11} + 6 q^{13} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.