Properties

Label 38640.o
Number of curves $4$
Conductor $38640$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.o1 38640bf4 \([0, -1, 0, -68696, -6907344]\) \(8753151307882969/65205\) \(267079680\) \([2]\) \(90112\) \(1.2115\)  
38640.o2 38640bf2 \([0, -1, 0, -4296, -106704]\) \(2141202151369/5832225\) \(23888793600\) \([2, 2]\) \(45056\) \(0.86491\)  
38640.o3 38640bf3 \([0, -1, 0, -2616, -192720]\) \(-483551781049/3672913125\) \(-15044252160000\) \([2]\) \(90112\) \(1.2115\)  
38640.o4 38640bf1 \([0, -1, 0, -376, -80]\) \(1439069689/828345\) \(3392901120\) \([2]\) \(22528\) \(0.51833\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 38640.2.a.o

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