Properties

Label 4704x
Number of curves $1$
Conductor $4704$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 4704x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.p1 4704x1 \([0, -1, 0, 19, -27]\) \(3584/3\) \(-602112\) \([]\) \(960\) \(-0.20329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4704x do not have complex multiplication.

Modular form 4704.2.a.x

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