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Properties

Label 422142y
Number of curves $2$
Conductor $422142$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("y1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 422142y have rank \(1\).

Complex multiplication

The elliptic curves in class 422142y do not have complex multiplication.

Modular form 422142.2.a.y

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

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 422142y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.y2 422142y1 \([1, 0, 1, -12884600, -985651198]\) \(3020743134142393/1742767615764\) \(136477849106298067569684\) \([3]\) \(48646656\) \(3.1287\) \(\Gamma_0(N)\)-optimal
422142.y1 422142y2 \([1, 0, 1, -737611955, -7710661607410]\) \(566741302835994084073/2796989208384\) \(219034980728875265795904\) \([]\) \(145939968\) \(3.6780\)