Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 34969.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34969.f1 34969g2 [1, 0, 0, -88151, 39371674] [] 315744  
34969.f2 34969g1 [1, 0, 0, -8676, -311783] [] 28704 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 34969.2.a.f

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

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.