Properties

Label 33509.a
Number of curves $1$
Conductor $33509$
CM no
Rank $3$

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

Elliptic curves in class 33509.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33509.a1 33509a1 \([0, 1, 1, -22, 32]\) \(1231925248/33509\) \(33509\) \([]\) \(7024\) \(-0.35157\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33509.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 33509.a do not have complex multiplication.

Modular form 33509.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} + 4 q^{6} - q^{7} + q^{9} + 6 q^{10} - 5 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display