Properties

Label 189618.z
Number of curves $1$
Conductor $189618$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.z1 189618n1 \([1, 1, 1, 4306, -21013]\) \(309147739823/186772608\) \(-5334412457088\) \([]\) \(387072\) \(1.1313\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 189618.z do not have complex multiplication.

Modular form 189618.2.a.z

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