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Properties

Label 105222k
Number of curves $2$
Conductor $105222$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 105222k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
105222.l2 105222k1 \([1, 0, 0, 16466454, -21440352348]\) \(493769165839269808367640671/484356987417093822480384\) \(-484356987417093822480384\) \([7]\) \(12512640\) \(3.2318\) \(\Gamma_0(N)\)-optimal
105222.l1 105222k2 \([1, 0, 0, -11682947706, -486046291388268]\) \(-176352252185278046480312672913502369/520483235310766404806064\) \(-520483235310766404806064\) \([]\) \(87588480\) \(4.2047\)  

Rank

sage: E.rank()
 

The elliptic curves in class 105222k have rank \(1\).

Complex multiplication

The elliptic curves in class 105222k do not have complex multiplication.

Modular form 105222.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.