Properties

Label 1600.r
Number of curves $1$
Conductor $1600$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 1600.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1600.r1 1600b1 \([0, 1, 0, -33, -97]\) \(-5000\) \(-819200\) \([]\) \(192\) \(-0.14256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1600.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1600.r do not have complex multiplication.

Modular form 1600.2.a.r

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