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Properties

Label 122010.l
Number of curves $2$
Conductor $122010$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 122010.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.l1 122010k2 \([1, 1, 0, -148642, -20852894]\) \(3087199234101529/199326394890\) \(23450551032413610\) \([2]\) \(1474560\) \(1.8914\)  
122010.l2 122010k1 \([1, 1, 0, -28592, 1452396]\) \(21973174804729/4842576900\) \(569724329708100\) \([2]\) \(737280\) \(1.5448\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 122010.l have rank \(0\).

Complex multiplication

The elliptic curves in class 122010.l do not have complex multiplication.

Modular form 122010.2.a.l

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