Properties

Label 33600eo
Number of curves $4$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.ca4 33600eo1 \([0, -1, 0, -40003908, 96203669562]\) \(7079962908642659949376/100085966990454375\) \(100085966990454375000000\) \([2]\) \(5160960\) \(3.2181\) \(\Gamma_0(N)\)-optimal
33600.ca2 33600eo2 \([0, -1, 0, -637875033, 6201065726937]\) \(448487713888272974160064/91549016015625\) \(5859137025000000000000\) \([2, 2]\) \(10321920\) \(3.5647\)  
33600.ca3 33600eo3 \([0, -1, 0, -635688033, 6245695835937]\) \(-55486311952875723077768/801237030029296875\) \(-410233359375000000000000000\) \([2]\) \(20643840\) \(3.9113\)  
33600.ca1 33600eo4 \([0, -1, 0, -10206000033, 396858041351937]\) \(229625675762164624948320008/9568125\) \(4898880000000000\) \([2]\) \(20643840\) \(3.9113\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600eo have rank \(0\).

Complex multiplication

The elliptic curves in class 33600eo do not have complex multiplication.

Modular form 33600.2.a.eo

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.