Properties

Label 429429ct
Number of curves $1$
Conductor $429429$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 429429ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.ct1 429429ct1 \([1, 1, 0, -544183, 154661434]\) \(-30515071121161/85766121\) \(-50091178853284569\) \([]\) \(5318784\) \(2.0767\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429ct1 has rank \(2\).

Complex multiplication

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

Modular form 429429.2.a.ct

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