Properties

Label 412224.bk
Number of curves $1$
Conductor $412224$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 412224.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.bk1 412224bk1 \([0, -1, 0, -2129, 129201]\) \(-65168050768/397609371\) \(-6514431934464\) \([]\) \(1032192\) \(1.1424\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224.bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 412224.bk do not have complex multiplication.

Modular form 412224.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} - 3 q^{7} + q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 5 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display