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Properties

Label 274890.a
Number of curves $2$
Conductor $274890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 274890.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.a1 274890a2 \([1, 1, 0, -162803, -25341147]\) \(11825859922687/5722200\) \(230911409975400\) \([2]\) \(2150400\) \(1.7104\)  
274890.a2 274890a1 \([1, 1, 0, -11883, -258243]\) \(4599141247/1974720\) \(79687074815040\) \([2]\) \(1075200\) \(1.3638\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 274890.a have rank \(0\).

Complex multiplication

The elliptic curves in class 274890.a do not have complex multiplication.

Modular form 274890.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} + q^{15} + q^{16} - q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.