Properties

Label 8470.w
Number of curves $1$
Conductor $8470$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.w1 8470s1 \([1, 1, 1, 14, 639]\) \(2496791/1433600\) \(-173465600\) \([]\) \(2496\) \(0.26002\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.w1 has rank \(1\).

Complex multiplication

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

Modular form 8470.2.a.w

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