Properties

Label 5550h
Number of curves $1$
Conductor $5550$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 5550h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.a1 5550h1 \([1, 1, 0, -75, 225]\) \(-76215625/1332\) \(-832500\) \([]\) \(1632\) \(-0.066467\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5550h1 has rank \(2\).

Complex multiplication

The elliptic curves in class 5550h do not have complex multiplication.

Modular form 5550.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} - 4 q^{13} + 4 q^{14} + q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display