Properties

Label 8670.q
Number of curves $1$
Conductor $8670$
CM no
Rank $1$

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

Elliptic curves in class 8670.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8670.q1 8670s1 \([1, 1, 1, 45, 6225]\) \(34822511/57600000\) \(-16646400000\) \([]\) \(7920\) \(0.64026\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8670.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8670.q do not have complex multiplication.

Modular form 8670.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 5 q^{13} - 3 q^{14} - q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display