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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 274890k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.k2 274890k1 \([1, 1, 0, -19058673, -42408801567]\) \(-18972272930584701727/8267129411062500\) \(-333608491272157577437500\) \([2]\) \(50577408\) \(3.2210\) \(\Gamma_0(N)\)-optimal
274890.k1 274890k2 \([1, 1, 0, -331617423, -2324275211817]\) \(99943228448001537681727/11290335851990250\) \(455605775869224716331750\) \([2]\) \(101154816\) \(3.5676\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 274890.2.a.k

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