Properties

Label 38640.cu
Number of curves $2$
Conductor $38640$
CM no
Rank $1$
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Show commands: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cu1 38640cx2 \([0, 1, 0, -11800, -3052]\) \(44365623586201/25674468750\) \(105162624000000\) \([2]\) \(110592\) \(1.3800\)  
38640.cu2 38640cx1 \([0, 1, 0, -8120, 278100]\) \(14457238157881/49990500\) \(204761088000\) \([2]\) \(55296\) \(1.0334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38640.cu have rank \(1\).

Complex multiplication

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

Modular form 38640.2.a.cu

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