Properties

Label 52800v
Number of curves 4
Conductor 52800
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("52800.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52800v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52800.d3 52800v1 [0, -1, 0, -10433, -403263] [2] 98304 \(\Gamma_0(N)\)-optimal
52800.d2 52800v2 [0, -1, 0, -18433, 308737] [2, 2] 196608  
52800.d4 52800v3 [0, -1, 0, 69567, 2332737] [2] 393216  
52800.d1 52800v4 [0, -1, 0, -234433, 43724737] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 52800v have rank \(1\).

Modular form 52800.2.a.d

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 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.