Properties

Label 33640a
Number of curves 2
Conductor 33640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33640.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33640a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.c2 33640a1 [0, 1, 0, -9531, -191966] [2] 107520 \(\Gamma_0(N)\)-optimal
33640.c1 33640a2 [0, 1, 0, -131476, -18386160] [2] 215040  

Rank

sage: E.rank()
 

The elliptic curves in class 33640a have rank \(1\).

Modular form 33640.2.a.c

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

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 Cremona 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 Cremona labels.