Properties

Label 3006f
Number of curves $1$
Conductor $3006$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 3006f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3006.c1 3006f1 \([1, -1, 1, 5071, -45471]\) \(19785968032823/12608077824\) \(-9191288733696\) \([]\) \(8832\) \(1.1764\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3006f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3006f do not have complex multiplication.

Modular form 3006.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3 q^{5} + 3 q^{7} + q^{8} - 3 q^{10} - 6 q^{11} + 2 q^{13} + 3 q^{14} + q^{16} + O(q^{20})\) Copy content Toggle raw display