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Properties

Label 281554cl
Number of curves $2$
Conductor $281554$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 281554cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281554.cl2 281554cl1 \([1, 0, 0, 260679, 9960313]\) \(3449795831/2071552\) \(-1176370684804037632\) \([2]\) \(8294400\) \(2.1567\) \(\Gamma_0(N)\)-optimal
281554.cl1 281554cl2 \([1, 0, 0, -1064281, 80183193]\) \(234770924809/130960928\) \(74368684229955254048\) \([2]\) \(16588800\) \(2.5033\)  

Rank

sage: E.rank()
 

The elliptic curves in class 281554cl have rank \(0\).

Complex multiplication

The elliptic curves in class 281554cl do not have complex multiplication.

Modular form 281554.2.a.cl

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