Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 429429s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.s1 429429s1 \([1, 1, 1, -33852959, -315845203354]\) \(-118436464005435433/1120962830293089\) \(-40608729112573088752406121\) \([]\) \(80011008\) \(3.5962\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429s1 has rank \(1\).

Complex multiplication

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

Modular form 429429.2.a.s

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