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Properties

Label 47610y
Number of curves $2$
Conductor $47610$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 47610y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.v2 47610y1 \([1, -1, 0, -1134, 19840]\) \(-18191447/8100\) \(-71844918300\) \([2]\) \(61440\) \(0.79008\) \(\Gamma_0(N)\)-optimal
47610.v1 47610y2 \([1, -1, 0, -19764, 1074298]\) \(96260823287/11250\) \(99784608750\) \([2]\) \(122880\) \(1.1367\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47610y have rank \(2\).

Complex multiplication

The elliptic curves in class 47610y do not have complex multiplication.

Modular form 47610.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 6 q^{11} - 6 q^{13} + q^{16} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.