Properties

Label 8002.a
Number of curves $1$
Conductor $8002$
CM no
Rank $1$

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

Elliptic curves in class 8002.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8002.a1 8002b1 \([1, 1, 1, 10, 3]\) \(109902239/64016\) \(-64016\) \([]\) \(480\) \(-0.38833\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8002.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8002.a do not have complex multiplication.

Modular form 8002.2.a.a

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