Properties

Label 10082g
Number of curves $1$
Conductor $10082$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 10082g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10082.g1 10082g1 \([1, -1, 0, -13238611, -18460412875]\) \(2003092024307193/9529458688\) \(1220726363546240155648\) \([]\) \(1632960\) \(2.8954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10082g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 10082g do not have complex multiplication.

Modular form 10082.2.a.g

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