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Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 122010.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.o1 122010o2 \([1, 1, 0, -167507, -26457171]\) \(4418129129836969/39680640\) \(4668387615360\) \([2]\) \(1032192\) \(1.5964\)  
122010.o2 122010o1 \([1, 1, 0, -10707, -397011]\) \(1153990560169/101990400\) \(11999068569600\) \([2]\) \(516096\) \(1.2498\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 122010.2.a.o

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