Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bb1 8470r1 \([1, 0, 0, -41, -175]\) \(-63088729/68600\) \(-8300600\) \([]\) \(1728\) \(0.022461\) \(\Gamma_0(N)\)-optimal
8470.bb2 8470r2 \([1, 0, 0, 344, 3136]\) \(37199299511/56000000\) \(-6776000000\) \([]\) \(5184\) \(0.57177\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8470.2.a.bb

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