Properties

Label 210826.k
Number of curves $2$
Conductor $210826$
CM no
Rank $1$
Graph

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

Elliptic curves in class 210826.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
210826.k1 210826f2 \([1, 1, 1, -321059, -70154219]\) \(1426487591593/2156\) \(5531706137804\) \([2]\) \(1622016\) \(1.7131\)  
210826.k2 210826f1 \([1, 1, 1, -19879, -1123763]\) \(-338608873/13552\) \(-34770724294768\) \([2]\) \(811008\) \(1.3666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 210826.k have rank \(1\).

Complex multiplication

The elliptic curves in class 210826.k do not have complex multiplication.

Modular form 210826.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} + 2 q^{6} - q^{7} + q^{8} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} - q^{14} - 4 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.