Properties

Label 116886w
Number of curves $4$
Conductor $116886$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.p4 116886w1 \([1, 0, 1, -72482, 12245924]\) \(-23771111713777/22848457968\) \(-40477437046248048\) \([2]\) \(1228800\) \(1.8828\) \(\Gamma_0(N)\)-optimal
116886.p3 116886w2 \([1, 0, 1, -1352662, 605225300]\) \(154502321244119857/55101928644\) \(97616427810493284\) \([2, 2]\) \(2457600\) \(2.2294\)  
116886.p2 116886w3 \([1, 0, 1, -1547472, 419454484]\) \(231331938231569617/90942310746882\) \(161109850969057022802\) \([2]\) \(4915200\) \(2.5759\)  
116886.p1 116886w4 \([1, 0, 1, -21640732, 38746796900]\) \(632678989847546725777/80515134\) \(142637471304174\) \([2]\) \(4915200\) \(2.5759\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886w have rank \(1\).

Complex multiplication

The elliptic curves in class 116886w do not have complex multiplication.

Modular form 116886.2.a.w

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