Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 429429.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.f1 429429f1 \([0, -1, 1, 38478202, 96715528106]\) \(736803680768000/899079608427\) \(-7688017664976091280360523\) \([]\) \(132088320\) \(3.4613\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429.f1 has rank \(1\).

Complex multiplication

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

Modular form 429429.2.a.f

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