Properties

Label 8470.v
Number of curves $2$
Conductor $8470$
CM no
Rank $1$
Graph

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

Elliptic curves in class 8470.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.v1 8470bg2 \([1, 0, 0, -102550, -12089868]\) \(67324767141241/3368750000\) \(5967946118750000\) \([2]\) \(61440\) \(1.7858\)  
8470.v2 8470bg1 \([1, 0, 0, 3930, -739100]\) \(3789119879/135520000\) \(-240081946720000\) \([2]\) \(30720\) \(1.4393\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8470.v have rank \(1\).

Complex multiplication

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

Modular form 8470.2.a.v

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