Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("18496.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.q1 18496d2 [0, -1, 0, -55873, 4889409] [2] 73728  
18496.q2 18496d1 [0, -1, 0, -9633, -261727] [2] 36864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 18496.2.a.q

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

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 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.