Properties

Label 8050.q
Number of curves $1$
Conductor $8050$
CM no
Rank $1$

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

Elliptic curves in class 8050.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8050.q1 8050r1 \([1, -1, 1, 6695, 4249947]\) \(84972077055/20040095362\) \(-7828162250781250\) \([]\) \(40320\) \(1.7289\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8050.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8050.q do not have complex multiplication.

Modular form 8050.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{9} + 4 q^{11} - 3 q^{13} - q^{14} + q^{16} - q^{17} - 3 q^{18} + O(q^{20})\) Copy content Toggle raw display