Properties

Label 8470.p
Number of curves $1$
Conductor $8470$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.p1 8470p1 \([1, -1, 0, -280924, 57381968]\) \(-11437987859001/358400\) \(-76826222950400\) \([]\) \(116160\) \(1.7606\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.p1 has rank \(0\).

Complex multiplication

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

Modular form 8470.2.a.p

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