Properties

Label 116886.v
Number of curves $2$
Conductor $116886$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.v1 116886t2 \([1, 0, 1, -1734296, -879233434]\) \(-39402364010111991625/3532128768\) \(-51713897292288\) \([]\) \(1804032\) \(2.0697\)  
116886.v2 116886t1 \([1, 0, 1, -19121, -1475476]\) \(-52802213121625/33540304392\) \(-491063596603272\) \([3]\) \(601344\) \(1.5204\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116886.v have rank \(0\).

Complex multiplication

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

Modular form 116886.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{12} - q^{13} - q^{14} + q^{16} - 6q^{17} - q^{18} + 5q^{19} + O(q^{20})\)  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.