Properties

Label 43.a
Number of curves $1$
Conductor $43$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 43.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43.a1 43a1 \([0, 1, 1, 0, 0]\) \(-4096/43\) \(-43\) \([]\) \(2\) \(-1.0044\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 43.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 43.a do not have complex multiplication.

Modular form 43.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} + 4 q^{6} + q^{9} + 8 q^{10} + 3 q^{11} - 4 q^{12} - 5 q^{13} + 8 q^{15} - 4 q^{16} - 3 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display