Properties

Label 8470.o
Number of curves $2$
Conductor $8470$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.o1 8470n1 \([1, 0, 1, -16943, 2456056]\) \(-2509090441/10718750\) \(-2297659255718750\) \([3]\) \(57024\) \(1.6326\) \(\Gamma_0(N)\)-optimal
8470.o2 8470n2 \([1, 0, 1, 149432, -59235794]\) \(1721540467559/8070721400\) \(-1730030808166753400\) \([]\) \(171072\) \(2.1819\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8470.o have rank \(0\).

Complex multiplication

The elliptic curves in class 8470.o do not have complex multiplication.

Modular form 8470.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} - 2q^{9} - q^{10} + q^{12} + 5q^{13} - q^{14} + q^{15} + q^{16} + 2q^{18} + 5q^{19} + O(q^{20})\)  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.