Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.n1 8470k1 \([1, 0, 1, -4821853, -4076792744]\) \(-57839429434456681/16470860000\) \(-3530675118707660000\) \([]\) \(295680\) \(2.5396\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.n1 has rank \(1\).

Complex multiplication

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

Modular form 8470.2.a.n

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