Properties

Label 52800.dd
Number of curves $2$
Conductor $52800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 52800.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52800.dd1 52800es1 \([0, -1, 0, -833, -2463]\) \(62500/33\) \(33792000000\) \([2]\) \(36864\) \(0.71185\) \(\Gamma_0(N)\)-optimal
52800.dd2 52800es2 \([0, -1, 0, 3167, -22463]\) \(1714750/1089\) \(-2230272000000\) \([2]\) \(73728\) \(1.0584\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 52800.2.a.dd

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} + q^{11} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.