Properties

Label 8050r
Number of curves $1$
Conductor $8050$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8050r

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 8050r1 has rank \(1\).

Complex multiplication

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

Modular form 8050.2.a.r

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