Properties

Label 122010i
Number of curves $4$
Conductor $122010$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 122010i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.k4 122010i1 \([1, 1, 0, 5176433, 1438819621]\) \(130384850244802923671/83033078421600000\) \(-9768758643222818400000\) \([2]\) \(10321920\) \(2.9084\) \(\Gamma_0(N)\)-optimal
122010.k3 122010i2 \([1, 1, 0, -21828447, 11770886709]\) \(9776964066308570159209/5148417725156250000\) \(605706196946907656250000\) \([2, 2]\) \(20643840\) \(3.2550\)  
122010.k2 122010i3 \([1, 1, 0, -199719027, -1077737759559]\) \(7488482171405468850635689/69244766235351562500\) \(8146577502822875976562500\) \([2]\) \(41287680\) \(3.6016\)  
122010.k1 122010i4 \([1, 1, 0, -276015947, 1763071924209]\) \(19766874175324764437159209/23734672172022037500\) \(2792360446366220689837500\) \([2]\) \(41287680\) \(3.6016\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 122010.2.a.i

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.