Properties

Label 286650r
Number of curves $1$
Conductor $286650$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 286650r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.r1 286650r1 \([1, -1, 0, -1655082, -729633164]\) \(4772330903305/570306048\) \(59918348461754764800\) \([]\) \(12337920\) \(2.5259\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 286650r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 286650r do not have complex multiplication.

Modular form 286650.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 5 q^{11} + q^{13} + q^{16} - 2 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display