Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 429429r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.r1 429429r1 \([1, 1, 1, -89178515, 326281490426]\) \(-1109873716015912969/8645553420777\) \(-610975299733770150292113\) \([]\) \(112783104\) \(3.3932\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429r1 has rank \(0\).

Complex multiplication

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

Modular form 429429.2.a.r

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