Properties

Label 429429cz
Number of curves $1$
Conductor $429429$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 429429cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.cz1 429429cz1 \([1, 1, 0, 504, 24237]\) \(24167/441\) \(-257563355049\) \([]\) \(508032\) \(0.86999\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429cz1 has rank \(1\).

Complex multiplication

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

Modular form 429429.2.a.cz

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