Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bg1 8470t2 \([1, 1, 1, -8896, 318979]\) \(43949604889/42350\) \(75025608350\) \([2]\) \(15360\) \(1.0079\)  
8470.bg2 8470t1 \([1, 1, 1, -426, 7283]\) \(-4826809/10780\) \(-19097427580\) \([2]\) \(7680\) \(0.66136\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8470.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} - q^{7} + q^{8} + q^{9} - q^{10} + 2q^{12} - 2q^{13} - q^{14} - 2q^{15} + q^{16} - 2q^{17} + q^{18} - 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.