Properties

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

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

Elliptic curves in class 281554.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281554.dd1 281554dd2 \([1, -1, 1, -67801, -2973785]\) \(60698457/28322\) \(16083192956305202\) \([2]\) \(1806336\) \(1.8042\)  
281554.dd2 281554dd1 \([1, -1, 1, 15009, -356989]\) \(658503/476\) \(-270305763971516\) \([2]\) \(903168\) \(1.4576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 281554.2.a.dd

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