Properties

Label 141610s
Number of curves $4$
Conductor $141610$
CM no
Rank $1$
Graph

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

Elliptic curves in class 141610s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.cg4 141610s1 \([1, -1, 1, 32747, 3625437]\) \(1367631/2800\) \(-7951330394786800\) \([2]\) \(983040\) \(1.7354\) \(\Gamma_0(N)\)-optimal
141610.cg3 141610s2 \([1, -1, 1, -250473, 39084581]\) \(611960049/122500\) \(347870704771922500\) \([2, 2]\) \(1966080\) \(2.0820\)  
141610.cg1 141610s3 \([1, -1, 1, -3790723, 2841546481]\) \(2121328796049/120050\) \(340913290676484050\) \([2]\) \(3932160\) \(2.4286\)  
141610.cg2 141610s4 \([1, -1, 1, -1241743, -497390743]\) \(74565301329/5468750\) \(15529942177317968750\) \([2]\) \(3932160\) \(2.4286\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141610s have rank \(1\).

Complex multiplication

The elliptic curves in class 141610s do not have complex multiplication.

Modular form 141610.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - 3 q^{9} - q^{10} - 4 q^{11} + 6 q^{13} + q^{16} - 3 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.