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Properties

Label 47610cn
Number of curves $2$
Conductor $47610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 47610cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.bw2 47610cn1 \([1, -1, 1, -59612, -10121349]\) \(-217081801/285660\) \(-30827902465718460\) \([2]\) \(608256\) \(1.8568\) \(\Gamma_0(N)\)-optimal
47610.bw1 47610cn2 \([1, -1, 1, -1154642, -477042141]\) \(1577505447721/838350\) \(90473192018956350\) \([2]\) \(1216512\) \(2.2034\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47610cn have rank \(1\).

Complex multiplication

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

Modular form 47610.2.a.cn

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