Properties

Label 28322.f
Number of curves $1$
Conductor $28322$
CM no
Rank $2$

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

Elliptic curves in class 28322.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.f1 28322e1 \([1, 1, 0, -1306, 22184]\) \(-208537/68\) \(-80426379908\) \([]\) \(27648\) \(0.80507\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28322.f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 28322.f do not have complex multiplication.

Modular form 28322.2.a.f

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