Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("en1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.ch3 33600en1 \([0, -1, 0, -908, 5562]\) \(82881856/36015\) \(36015000000\) \([2]\) \(36864\) \(0.72173\) \(\Gamma_0(N)\)-optimal
33600.ch2 33600en2 \([0, -1, 0, -7033, -221063]\) \(601211584/11025\) \(705600000000\) \([2, 2]\) \(73728\) \(1.0683\)  
33600.ch4 33600en3 \([0, -1, 0, -33, -648063]\) \(-8/354375\) \(-181440000000000\) \([2]\) \(147456\) \(1.4149\)  
33600.ch1 33600en4 \([0, -1, 0, -112033, -14396063]\) \(303735479048/105\) \(53760000000\) \([2]\) \(147456\) \(1.4149\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33600.2.a.en

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.