Properties

Label 116886.t
Number of curves $2$
Conductor $116886$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.t1 116886o2 \([1, 0, 1, -16046066, 24738734612]\) \(3776104682692733708238625/3408048\) \(412373808\) \([]\) \(2488320\) \(2.3332\)  
116886.t2 116886o1 \([1, 0, 1, -198146, 33903956]\) \(7110352307247726625/6866458324992\) \(830841457324032\) \([]\) \(829440\) \(1.7839\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116886.t have rank \(2\).

Complex multiplication

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

Modular form 116886.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + q^{12} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - q^{18} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.