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Properties

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

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 122010.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.n1 122010m2 \([1, 1, 0, -2204682, 616329876]\) \(29368348751959183/12916875000000\) \(521242497418125000000\) \([2]\) \(7956480\) \(2.6711\)  
122010.n2 122010m1 \([1, 1, 0, -1875402, 987296724]\) \(18076936743188623/9561600000\) \(385845048691200000\) \([2]\) \(3978240\) \(2.3245\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 122010.2.a.n

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