Properties

Label 33640.a
Number of curves 2
Conductor 33640
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("33640.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33640.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.a1 33640e2 [0, 1, 0, -568796, -165191120] [2] 322560  
33640.a2 33640e1 [0, 1, 0, -43171, -1406370] [2] 161280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33640.a have rank \(0\).

Modular form 33640.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} - 4q^{7} + q^{9} - 2q^{13} + 2q^{15} + 4q^{17} + O(q^{20}) \)

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.