Properties

Label 433200.id
Number of curves $4$
Conductor $433200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("id1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 433200.id

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.id1 433200id4 \([0, 1, 0, -89675408, -326412040812]\) \(26487576322129/44531250\) \(134080760850000000000000\) \([2]\) \(53084160\) \(3.3330\)  
433200.id2 433200id2 \([0, 1, 0, -7367408, -1624672812]\) \(14688124849/8122500\) \(24456330779040000000000\) \([2, 2]\) \(26542080\) \(2.9864\)  
433200.id3 433200id1 \([0, 1, 0, -4479408, 3625711188]\) \(3301293169/22800\) \(68649349555200000000\) \([2]\) \(13271040\) \(2.6399\) \(\Gamma_0(N)\)-optimal*
433200.id4 433200id3 \([0, 1, 0, 28732592, -12815672812]\) \(871257511151/527800050\) \(-1589172374022019200000000\) \([2]\) \(53084160\) \(3.3330\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 433200.id1.

Rank

sage: E.rank()
 

The elliptic curves in class 433200.id have rank \(0\).

Complex multiplication

The elliptic curves in class 433200.id do not have complex multiplication.

Modular form 433200.2.a.id

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.