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Properties

Label 47190.bo
Number of curves $1$
Conductor $47190$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bo1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 47190.bo1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(11\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 7 T + 23 T^{2}\) 1.23.ah
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 47190.bo do not have complex multiplication.

Modular form 47190.2.a.bo

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - 2 q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 47190.bo

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.bo1 47190bo1 \([1, 1, 1, -893406, -518210307]\) \(-3040489341769/2706725970\) \(-70205500762443587970\) \([]\) \(1552320\) \(2.5052\) \(\Gamma_0(N)\)-optimal