Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.dc1 38640db2 \([0, 1, 0, -63680, -6202572]\) \(6972359126281921/5071500000\) \(20772864000000\) \([2]\) \(184320\) \(1.4900\)  
38640.dc2 38640db1 \([0, 1, 0, -4800, -55500]\) \(2986606123201/1421952000\) \(5824315392000\) \([2]\) \(92160\) \(1.1434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 38640.2.a.dc

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