Properties

Label 53824.y
Number of curves $2$
Conductor $53824$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 53824.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53824.y1 53824u2 \([0, 1, 0, -24491041, 46958951263]\) \(-10418796526321/82044596\) \(-12793161728084755349504\) \([]\) \(3225600\) \(3.0705\)  
53824.y2 53824u1 \([0, 1, 0, 267999, -88607137]\) \(13651919/29696\) \(-4630478412950011904\) \([]\) \(645120\) \(2.2658\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53824.y have rank \(0\).

Complex multiplication

The elliptic curves in class 53824.y do not have complex multiplication.

Modular form 53824.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2 q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - q^{15} - 8 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.