Properties

Label 18928.j
Number of curves $2$
Conductor $18928$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 18928.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18928.j1 18928y2 \([0, -1, 0, -992, 12544]\) \(-156116857/2744\) \(-1899462656\) \([]\) \(10368\) \(0.57771\)  
18928.j2 18928y1 \([0, -1, 0, 48, 64]\) \(17303/14\) \(-9691136\) \([]\) \(3456\) \(0.028402\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 18928.2.a.j

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.