Properties

Label 33600em
Number of curves $6$
Conductor $33600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 33600em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.ce6 33600em1 \([0, -1, 0, 1567, 4737]\) \(103823/63\) \(-258048000000\) \([2]\) \(32768\) \(0.87892\) \(\Gamma_0(N)\)-optimal
33600.ce5 33600em2 \([0, -1, 0, -6433, 44737]\) \(7189057/3969\) \(16257024000000\) \([2, 2]\) \(65536\) \(1.2255\)  
33600.ce3 33600em3 \([0, -1, 0, -62433, -5947263]\) \(6570725617/45927\) \(188116992000000\) \([2]\) \(131072\) \(1.5721\)  
33600.ce2 33600em4 \([0, -1, 0, -78433, 8468737]\) \(13027640977/21609\) \(88510464000000\) \([2, 2]\) \(131072\) \(1.5721\)  
33600.ce4 33600em5 \([0, -1, 0, -54433, 13724737]\) \(-4354703137/17294403\) \(-70837874688000000\) \([2]\) \(262144\) \(1.9186\)  
33600.ce1 33600em6 \([0, -1, 0, -1254433, 541196737]\) \(53297461115137/147\) \(602112000000\) \([2]\) \(262144\) \(1.9186\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33600.2.a.em

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 4 q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.