Properties

Label 52800.hs
Number of curves 4
Conductor 52800
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("52800.hs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800.hs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.hs1 52800hf4 [0, 1, 0, -234433, -43724737] [2] 393216  
52800.hs2 52800hf2 [0, 1, 0, -18433, -308737] [2, 2] 196608  
52800.hs3 52800hf1 [0, 1, 0, -10433, 403263] [2] 98304 \(\Gamma_0(N)\)-optimal
52800.hs4 52800hf3 [0, 1, 0, 69567, -2332737] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 52800.hs have rank \(0\).

Modular form 52800.2.a.hs

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

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 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.