Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 429429.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
429429.b1 429429b1 \([0, -1, 1, -1966774, -1192635390]\) \(-14764896256/2250423\) \(-128239278611635121931\) \([]\) \(26002944\) \(2.5876\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 429429.b1 has rank \(0\).

Complex multiplication

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

Modular form 429429.2.a.b

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