Properties

Label 116688.n
Number of curves $2$
Conductor $116688$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116688.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116688.n1 116688l1 \([0, -1, 0, -1496, 16368]\) \(90458382169/25788048\) \(105627844608\) \([2]\) \(153600\) \(0.82190\) \(\Gamma_0(N)\)-optimal
116688.n2 116688l2 \([0, -1, 0, 3944, 103408]\) \(1656015369191/2114999172\) \(-8663036608512\) \([2]\) \(307200\) \(1.1685\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116688.n have rank \(1\).

Complex multiplication

The elliptic curves in class 116688.n do not have complex multiplication.

Modular form 116688.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{5} + q^{9} - q^{11} - q^{13} - 4q^{15} + q^{17} - 2q^{19} + O(q^{20})\)  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.