Properties

Label 20339b
Number of curves $1$
Conductor $20339$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 20339b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20339.b1 20339b1 \([1, 0, 0, -17, -16]\) \(294937/121\) \(223729\) \([]\) \(1680\) \(-0.27597\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20339b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 20339b do not have complex multiplication.

Modular form 20339.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} + 3 q^{8} - 2 q^{9} + 3 q^{10} - q^{11} - q^{12} - 3 q^{13} - q^{14} - 3 q^{15} - q^{16} - 3 q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display