Properties

Label 4704.f
Number of curves $1$
Conductor $4704$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 4704.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.f1 4704t1 \([0, -1, 0, 152864, -2188556]\) \(2731405432/1594323\) \(-230582674642650624\) \([]\) \(43680\) \(2.0210\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704.f1 has rank \(1\).

Complex multiplication

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

Modular form 4704.2.a.f

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