Properties

Label 858.g
Number of curves $1$
Conductor $858$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 858.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
858.g1 858g1 \([1, 1, 1, -46, 107]\) \(-10779215329/658944\) \(-658944\) \([]\) \(144\) \(-0.12877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 858.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 858.g do not have complex multiplication.

Modular form 858.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - q^{13} - 3 q^{14} + q^{15} + q^{16} - 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display