Properties

Label 4046.p
Number of curves $1$
Conductor $4046$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 4046.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4046.p1 4046s1 \([1, 0, 0, -345650, -78246124]\) \(654699641761/112\) \(781284833392\) \([]\) \(34272\) \(1.6806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4046.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 4046.p do not have complex multiplication.

Modular form 4046.2.a.p

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