Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.y1 8470w2 \([1, -1, 1, -99243, -12008719]\) \(45844273539/350\) \(825281691850\) \([2]\) \(42240\) \(1.4612\)  
8470.y2 8470w1 \([1, -1, 1, -6073, -194763]\) \(-10503459/980\) \(-2310788737180\) \([2]\) \(21120\) \(1.1146\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8470.2.a.y

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