Properties

Label 6019.a
Number of curves $1$
Conductor $6019$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 6019.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6019.a1 6019a1 \([0, 0, 1, 64, 599]\) \(28991029248/171908659\) \(-171908659\) \([]\) \(1100\) \(0.26213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6019.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6019.a do not have complex multiplication.

Modular form 6019.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 3 q^{5} - 3 q^{7} - 3 q^{9} - q^{11} + q^{13} + 4 q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display