Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bc1 8470y2 \([1, 0, 0, -78477396, -267593527024]\) \(-249353795628717731809/14000000\) \(-3001024334000000\) \([]\) \(798336\) \(2.8844\)  
8470.bc2 8470y1 \([1, 0, 0, -959956, -374215280]\) \(-456390127585249/17983078400\) \(-3854832562759270400\) \([3]\) \(266112\) \(2.3351\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8470.2.a.bc

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