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Properties

Label 282534.y
Number of curves $2$
Conductor $282534$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 282534.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
282534.y1 282534y2 \([1, 1, 0, -683771, 218454237]\) \(-16591834777/98304\) \(-209475633618714624\) \([]\) \(5524200\) \(2.1639\)  
282534.y2 282534y1 \([1, 1, 0, 22564, 1609392]\) \(596183/864\) \(-1841094436101984\) \([]\) \(1841400\) \(1.6146\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 282534.y have rank \(0\).

Complex multiplication

The elliptic curves in class 282534.y do not have complex multiplication.

Modular form 282534.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} + q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 4 q^{13} - 3 q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.