Properties

Label 416955.bk
Number of curves $1$
Conductor $416955$
CM no
Rank $1$

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

Elliptic curves in class 416955.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416955.bk1 416955bk1 \([0, 1, 1, -47411, -12859345]\) \(-250523582464/1369738755\) \(-64440566468818155\) \([]\) \(2815200\) \(1.9094\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 416955.bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416955.bk do not have complex multiplication.

Modular form 416955.2.a.bk

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