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Properties

Label 55506.bk
Number of curves $1$
Conductor $55506$
CM no
Rank $1$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 55506.bk1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(11\)\(1 - T\)
\(29\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - T + 5 T^{2}\) 1.5.ab
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 - 5 T + 19 T^{2}\) 1.19.af
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 55506.bk do not have complex multiplication.

Modular form 55506.2.a.bk

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - q^{14} + q^{15} + q^{16} + 3 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 55506.bk

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.bk1 55506bj1 \([1, 0, 0, -11591496710, -495388958772636]\) \(-11872994862835724607989/436955947638718464\) \(-6338983717419060037673828745216\) \([]\) \(125502720\) \(4.6814\) \(\Gamma_0(N)\)-optimal