Properties

Label 33800y
Number of curves 2
Conductor 33800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("33800.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33800y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.p2 33800y1 [0, 0, 0, -147875, -13731250] [2] 268800 \(\Gamma_0(N)\)-optimal
33800.p1 33800y2 [0, 0, 0, -992875, 370743750] [2] 537600  

Rank

sage: E.rank()
 

The elliptic curves in class 33800y have rank \(1\).

Modular form 33800.2.a.p

sage: E.q_eigenform(10)
 
\( q + 4q^{7} - 3q^{9} + 2q^{11} - 4q^{17} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.