Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8470.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.q1 8470bh1 \([1, -1, 1, -12, 399]\) \(-1459161/560000\) \(-67760000\) \([]\) \(5376\) \(0.18177\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8470.q1 has rank \(1\).

Complex multiplication

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

Modular form 8470.2.a.q

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