Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.g4 116886f1 \([1, 1, 0, 1807496, -13002183872]\) \(368637286278891167/41443067603976192\) \(-73418922287567666675712\) \([2]\) \(11059200\) \(3.0669\) \(\Gamma_0(N)\)-optimal
116886.g3 116886f2 \([1, 1, 0, -73154424, -233045403840]\) \(24439335640029940889953/902916953746891776\) \(1599572461496797341582336\) \([2, 2]\) \(22118400\) \(3.4135\)  
116886.g2 116886f3 \([1, 1, 0, -185810264, 657634198368]\) \(400476194988122984445793/126270124548858769248\) \(223695228115900790107756128\) \([2]\) \(44236800\) \(3.7601\)  
116886.g1 116886f4 \([1, 1, 0, -1159889304, -15204991845600]\) \(97413070452067229637409633/140666577176907936\) \(249199422130100200008096\) \([2]\) \(44236800\) \(3.7601\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 116886.2.a.f

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