Properties

Label 37440.bo
Number of curves $4$
Conductor $37440$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37440.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.bo1 37440bj4 \([0, 0, 0, -7788, 215152]\) \(2186875592/428415\) \(10233922682880\) \([2]\) \(49152\) \(1.2131\)  
37440.bo2 37440bj2 \([0, 0, 0, -2388, -41888]\) \(504358336/38025\) \(113542041600\) \([2, 2]\) \(24576\) \(0.86651\)  
37440.bo3 37440bj1 \([0, 0, 0, -2343, -43652]\) \(30488290624/195\) \(9097920\) \([2]\) \(12288\) \(0.51993\) \(\Gamma_0(N)\)-optimal
37440.bo4 37440bj3 \([0, 0, 0, 2292, -186032]\) \(55742968/658125\) \(-15721205760000\) \([2]\) \(49152\) \(1.2131\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37440.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 37440.bo do not have complex multiplication.

Modular form 37440.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.