Properties

Label 43669.a
Number of curves $1$
Conductor $43669$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 43669.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43669.a1 43669a1 \([0, 0, 1, -19, 30]\) \(758550528/43669\) \(43669\) \([]\) \(11176\) \(-0.35561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 43669.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 43669.a do not have complex multiplication.

Modular form 43669.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} + 6 q^{6} - 2 q^{7} + 6 q^{9} + 6 q^{10} - 6 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} - 4 q^{16} - q^{17} - 12 q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display