Properties

Label 38640.bo
Number of curves $2$
Conductor $38640$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38640.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.bo1 38640bz2 \([0, -1, 0, -1075760, -423182400]\) \(33613237452390629041/532385784000000\) \(2180652171264000000\) \([2]\) \(829440\) \(2.3192\)  
38640.bo2 38640bz1 \([0, -1, 0, -133680, 8667072]\) \(64500981545311921/29485596672000\) \(120773003968512000\) \([2]\) \(414720\) \(1.9726\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38640.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 38640.bo do not have complex multiplication.

Modular form 38640.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + 2q^{11} - 6q^{13} - q^{15} - 4q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.