Properties

Label 116160p
Number of curves $6$
Conductor $116160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 116160p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.ba5 116160p1 \([0, -1, 0, 38559, -11314719]\) \(13651919/126720\) \(-58849285877268480\) \([2]\) \(737280\) \(1.8990\) \(\Gamma_0(N)\)-optimal
116160.ba4 116160p2 \([0, -1, 0, -580961, -157397535]\) \(46694890801/3920400\) \(1820649781827993600\) \([2, 2]\) \(1474560\) \(2.2456\)  
116160.ba3 116160p3 \([0, -1, 0, -1974881, 887763681]\) \(1834216913521/329422500\) \(152985155278602240000\) \([2, 2]\) \(2949120\) \(2.5922\)  
116160.ba2 116160p4 \([0, -1, 0, -9099361, -10561771295]\) \(179415687049201/1443420\) \(670330146945761280\) \([2]\) \(2949120\) \(2.5922\)  
116160.ba6 116160p5 \([0, -1, 0, 3833119, 5119472481]\) \(13411719834479/32153832150\) \(-14932371056226769305600\) \([2]\) \(5898240\) \(2.9388\)  
116160.ba1 116160p6 \([0, -1, 0, -30085601, 63524069985]\) \(6484907238722641/283593750\) \(131702096486400000000\) \([2]\) \(5898240\) \(2.9388\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116160p have rank \(0\).

Complex multiplication

The elliptic curves in class 116160p do not have complex multiplication.

Modular form 116160.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{13} + q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.