Properties

Label 4002.r
Number of curves $1$
Conductor $4002$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.r1 4002p1 \([1, 0, 0, -1811224, 938072696]\) \(-657113243203147908283777/368184\) \(-368184\) \([]\) \(33120\) \(1.7821\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.r1 has rank \(0\).

Complex multiplication

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

Modular form 4002.2.a.r

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