Properties

Label 2809.a
Number of curves $1$
Conductor $2809$
CM no
Rank $1$

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

Elliptic curves in class 2809.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2809.a1 2809a1 \([1, -1, 0, 878, 50957]\) \(3375/53\) \(-1174711139837\) \([]\) \(5616\) \(0.99660\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2809.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2809.a do not have complex multiplication.

Modular form 2809.2.a.a

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