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Properties

Label 122010r
Number of curves $2$
Conductor $122010$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 122010r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.v2 122010r1 \([1, 0, 1, -38274, -2883884]\) \(18076936743188623/9561600000\) \(3279628800000\) \([2]\) \(568320\) \(1.3515\) \(\Gamma_0(N)\)-optimal
122010.v1 122010r2 \([1, 0, 1, -44994, -1803308]\) \(29368348751959183/12916875000000\) \(4430488125000000\) \([2]\) \(1136640\) \(1.6981\)  

Rank

sage: E.rank()
 

The elliptic curves in class 122010r have rank \(1\).

Complex multiplication

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

Modular form 122010.2.a.r

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 Cremona 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 Cremona labels.