Properties

Label 33609.a
Number of curves $1$
Conductor $33609$
CM no
Rank $3$

Related objects

Downloads

Learn more

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

Elliptic curves in class 33609.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33609.a1 33609a1 \([1, 1, 1, -232, 1262]\) \(1381352948353/1714059\) \(1714059\) \([]\) \(15616\) \(0.10550\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33609.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 33609.a do not have complex multiplication.

Modular form 33609.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 3 q^{5} + q^{6} - 5 q^{7} + 3 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + q^{12} - 5 q^{13} + 5 q^{14} + 3 q^{15} - q^{16} - q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display