Properties

Label 18496.a
Number of curves $2$
Conductor $18496$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18496.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.a1 18496h1 [0, 1, 0, -5009, 53647] [2] 36864 \(\Gamma_0(N)\)-optimal
18496.a2 18496h2 [0, 1, 0, 18111, 428191] [2] 73728  

Rank

sage: E.rank()
 

The elliptic curves in class 18496.a have rank \(1\).

Modular form 18496.2.a.a

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

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 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.