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Properties

Label 274890w
Number of curves $2$
Conductor $274890$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 274890w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.w1 274890w1 \([1, 1, 0, -416672, -103696116]\) \(68001744211490809/1022422500\) \(120286984702500\) \([2]\) \(3096576\) \(1.8383\) \(\Gamma_0(N)\)-optimal
274890.w2 274890w2 \([1, 1, 0, -404422, -110063666]\) \(-62178675647294809/8362782148050\) \(-983872956935934450\) \([2]\) \(6193152\) \(2.1849\)  

Rank

sage: E.rank()
 

The elliptic curves in class 274890w have rank \(1\).

Complex multiplication

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

Modular form 274890.2.a.w

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