Properties

Label 429429.g
Number of curves $1$
Conductor $429429$
CM no
Rank $2$

Related objects

Downloads

Learn more

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

Elliptic curves in class 429429.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.g1 429429g1 \([0, -1, 1, -810, 10064]\) \(-221360128/27783\) \(-7385749371\) \([]\) \(311040\) \(0.62774\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429.g1 has rank \(2\).

Complex multiplication

The elliptic curves in class 429429.g do not have complex multiplication.

Modular form 429429.2.a.g

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