Properties

Label 18496j
Number of curves $4$
Conductor $18496$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18496.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.k3 18496j1 [0, 0, 0, -12716, -235824] [2] 36864 \(\Gamma_0(N)\)-optimal
18496.k2 18496j2 [0, 0, 0, -105196, 12970320] [2, 2] 73728  
18496.k1 18496j3 [0, 0, 0, -1677356, 836153296] [2] 147456  
18496.k4 18496j4 [0, 0, 0, -12716, 34980560] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 18496j have rank \(0\).

Modular form 18496.2.a.k

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

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.