Properties

Label 492272n
Number of curves $1$
Conductor $492272$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 492272n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
492272.n1 492272n1 \([0, 0, 0, -496, -3856]\) \(3294646272/338437\) \(1386237952\) \([]\) \(545280\) \(0.48968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 492272n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 492272n do not have complex multiplication.

Modular form 492272.2.a.n

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