Properties

Label 8033.a
Number of curves $1$
Conductor $8033$
CM no
Rank $0$

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

Elliptic curves in class 8033.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8033.a1 8033a1 \([1, 0, 1, -555, -5073]\) \(-18857204627113/2225141\) \(-2225141\) \([]\) \(2128\) \(0.24358\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8033.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8033.a do not have complex multiplication.

Modular form 8033.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - 3 q^{5} + q^{6} + 2 q^{7} - 3 q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + q^{13} + 2 q^{14} - 3 q^{15} - q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display