Properties

Label 61710.n
Number of curves $2$
Conductor $61710$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 61710.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.n1 61710l1 \([1, 1, 0, -26732, 1544976]\) \(1587323326642451/132651000000\) \(176558481000000\) \([2]\) \(228096\) \(1.4757\) \(\Gamma_0(N)\)-optimal
61710.n2 61710l2 \([1, 1, 0, 28268, 7143976]\) \(1876752050077549/17596287801000\) \(-23420659063131000\) \([2]\) \(456192\) \(1.8222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61710.n have rank \(1\).

Complex multiplication

The elliptic curves in class 61710.n do not have complex multiplication.

Modular form 61710.2.a.n

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