Properties

Label 10005.n
Number of curves $1$
Conductor $10005$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 10005.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10005.n1 10005c1 \([0, -1, 1, -16, -3]\) \(481890304/250125\) \(250125\) \([]\) \(1440\) \(-0.27224\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10005.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10005.n do not have complex multiplication.

Modular form 10005.2.a.n

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