Properties

Label 161700dz
Number of curves $1$
Conductor $161700$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dz1")
 
E.isogeny_class()
 

Elliptic curves in class 161700dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.r1 161700dz1 \([0, -1, 0, 13067, -365903]\) \(327680000/264627\) \(-199251852307200\) \([]\) \(381024\) \(1.4317\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 161700dz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 161700dz do not have complex multiplication.

Modular form 161700.2.a.dz

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