Properties

Label 4002.p
Number of curves $1$
Conductor $4002$
CM no
Rank $1$

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

Elliptic curves in class 4002.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.p1 4002q1 \([1, 0, 0, -1326, -88956]\) \(-257854523348449/3260780423424\) \(-3260780423424\) \([]\) \(5760\) \(1.0828\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4002.p do not have complex multiplication.

Modular form 4002.2.a.p

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