Properties

Label 18928b
Number of curves $4$
Conductor $18928$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18928b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18928.n4 18928b1 [0, 0, 0, 169, -4394] [2] 9216 \(\Gamma_0(N)\)-optimal
18928.n3 18928b2 [0, 0, 0, -3211, -65910] [2, 2] 18432  
18928.n1 18928b3 [0, 0, 0, -50531, -4372030] [2] 36864  
18928.n2 18928b4 [0, 0, 0, -9971, 303186] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 18928b have rank \(1\).

Complex multiplication

The elliptic curves in class 18928b do not have complex multiplication.

Modular form 18928.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.