Properties

Label 41038.a
Number of curves $1$
Conductor $41038$
CM no
Rank $1$

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

Elliptic curves in class 41038.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41038.a1 41038b1 \([1, -1, 0, -758968, 253638976]\) \(2003092024307193/9529458688\) \(230017966614249472\) \([]\) \(1492992\) \(2.1806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41038.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41038.a do not have complex multiplication.

Modular form 41038.2.a.a

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