Properties

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

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 122010.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122010.dj1 122010do1 \([1, 0, 0, -312566640, -2126999407968]\) \(-68921624431417353829938395089/117227740275188640\) \(-5744159273484243360\) \([]\) \(20885760\) \(3.2892\) \(\Gamma_0(N)\)-optimal
122010.dj2 122010do2 \([1, 0, 0, 975016510, -11270628771900]\) \(2092008964199791878427102647311/2330581636033743421440000000\) \(-114198500165653427650560000000\) \([7]\) \(146200320\) \(4.2621\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 122010.2.a.dj

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.