Properties

Label 450840f
Number of curves $1$
Conductor $450840$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 450840f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.f1 450840f1 \([0, -1, 0, 300464, -37505735]\) \(7767586344704/6060234375\) \(-2340469206123750000\) \([]\) \(6967296\) \(2.2127\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 450840f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 450840f do not have complex multiplication.

Modular form 450840.2.a.f

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