Properties

Label 290605.k
Number of curves $2$
Conductor $290605$
CM no
Rank $1$
Graph

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

Elliptic curves in class 290605.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
290605.k1 290605k1 \([1, -1, 0, -58730, 5490951]\) \(476196576129/197225\) \(9278623880225\) \([2]\) \(870912\) \(1.4502\) \(\Gamma_0(N)\)-optimal
290605.k2 290605k2 \([1, -1, 0, -49705, 7229166]\) \(-288673724529/311181605\) \(-14639812758219005\) \([2]\) \(1741824\) \(1.7968\)  

Rank

sage: E.rank()
 

The elliptic curves in class 290605.k have rank \(1\).

Complex multiplication

The elliptic curves in class 290605.k do not have complex multiplication.

Modular form 290605.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} - q^{7} - 3 q^{8} - 3 q^{9} - q^{10} + 2 q^{11} - 4 q^{13} - q^{14} - q^{16} - 6 q^{17} - 3 q^{18} + O(q^{20})\) 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.