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Properties

Label 34969.k
Number of curves $2$
Conductor $34969$
CM no
Rank $0$
Graph

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

Elliptic curves in class 34969.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34969.k1 34969f2 \([1, 0, 1, -1049799, 413933375]\) \(-24729001\) \(-5174102280900289\) \([]\) \(315744\) \(2.0976\)  
34969.k2 34969f1 \([1, 0, 1, -729, -29647]\) \(-121\) \(-353398147729\) \([]\) \(28704\) \(0.89865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34969.k have rank \(0\).

Complex multiplication

The elliptic curves in class 34969.k do not have complex multiplication.

Modular form 34969.2.a.k

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

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.