Properties

Label 122199.g
Number of curves $1$
Conductor $122199$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 122199.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122199.g1 122199e1 \([1, 1, 0, -3426, -78879]\) \(-365679263951/1369599\) \(-16663911033\) \([]\) \(93312\) \(0.82114\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122199.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 122199.g do not have complex multiplication.

Modular form 122199.2.a.g

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