Properties

Label 61710u
Number of curves $2$
Conductor $61710$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 61710u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.u2 61710u1 \([1, 0, 1, -469439, -123744238]\) \(8595711443128766579/7520256000000\) \(10009460736000000\) \([2]\) \(1036800\) \(1.9959\) \(\Gamma_0(N)\)-optimal
61710.u1 61710u2 \([1, 0, 1, -7509439, -7921248238]\) \(35185850652034529726579/26967168000\) \(35893300608000\) \([2]\) \(2073600\) \(2.3425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61710u have rank \(0\).

Complex multiplication

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

Modular form 61710.2.a.u

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