Properties

Label 1710.s
Number of curves $2$
Conductor $1710$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1710.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1710.s1 1710r2 \([1, -1, 1, -14567, -673041]\) \(468898230633769/5540400\) \(4038951600\) \([2]\) \(3072\) \(0.99330\)  
1710.s2 1710r1 \([1, -1, 1, -887, -10929]\) \(-105756712489/12476160\) \(-9095120640\) \([2]\) \(1536\) \(0.64672\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1710.s have rank \(0\).

Complex multiplication

The elliptic curves in class 1710.s do not have complex multiplication.

Modular form 1710.2.a.s

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