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Properties

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

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 282534.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
282534.ce1 282534ce2 \([1, 1, 1, -135521, -19979233]\) \(-6329617441/279936\) \(-12173767291776384\) \([]\) \(2557800\) \(1.8515\)  
282534.ce2 282534ce1 \([1, 1, 1, -981, 26865]\) \(-2401/6\) \(-260926082214\) \([]\) \(365400\) \(0.87852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 282534.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} + q^{15} + q^{16} - 4 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.