Properties

Label 52800.d
Number of curves $4$
Conductor $52800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 52800.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52800.d1 52800v4 \([0, -1, 0, -234433, 43724737]\) \(347873904937/395307\) \(1619177472000000\) \([2]\) \(393216\) \(1.8318\)  
52800.d2 52800v2 \([0, -1, 0, -18433, 308737]\) \(169112377/88209\) \(361304064000000\) \([2, 2]\) \(196608\) \(1.4852\)  
52800.d3 52800v1 \([0, -1, 0, -10433, -403263]\) \(30664297/297\) \(1216512000000\) \([2]\) \(98304\) \(1.1387\) \(\Gamma_0(N)\)-optimal
52800.d4 52800v3 \([0, -1, 0, 69567, 2332737]\) \(9090072503/5845851\) \(-23944605696000000\) \([2]\) \(393216\) \(1.8318\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 52800.d do not have complex multiplication.

Modular form 52800.2.a.d

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