Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.d1 4002g1 \([1, 0, 1, -445, 3632]\) \(-9714044119753/194769336\) \(-194769336\) \([]\) \(2112\) \(0.38305\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.d1 has rank \(1\).

Complex multiplication

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

Modular form 4002.2.a.d

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