Properties

Label 429429.p
Number of curves $1$
Conductor $429429$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 429429.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.p1 429429p1 \([0, 1, 1, -45812576, -111389515792]\) \(5528367104/413343\) \(795044746311592864460373\) \([]\) \(168030720\) \(3.3315\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429.p1 has rank \(0\).

Complex multiplication

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

Modular form 429429.2.a.p

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