Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.e1 4002d1 \([1, 0, 1, -699, 14470]\) \(-37693095294889/69371756544\) \(-69371756544\) \([]\) \(3840\) \(0.77025\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.e1 has rank \(0\).

Complex multiplication

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

Modular form 4002.2.a.e

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