Properties

Label 47610v
Number of curves $2$
Conductor $47610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 47610v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.w2 47610v1 \([1, -1, 0, -1166544, -486749952]\) \(-1626794704081/8125440\) \(-876882559024880640\) \([2]\) \(1013760\) \(2.2904\) \(\Gamma_0(N)\)-optimal
47610.w1 47610v2 \([1, -1, 0, -18687024, -31088020320]\) \(6687281588245201/165600\) \(17871247806213600\) \([2]\) \(2027520\) \(2.6370\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47610v have rank \(0\).

Complex multiplication

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

Modular form 47610.2.a.v

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