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Properties

Label 278850.bg
Number of curves $1$
Conductor $278850$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 278850.bg1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(11\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 278850.bg do not have complex multiplication.

Modular form 278850.2.a.bg

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

Elliptic curves in class 278850.bg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
278850.bg1 278850bg1 \([1, 1, 0, -29548181900, -1955248485390000]\) \(-17218915986569071075813/2522559283200000\) \(-417976224016402022400000000000\) \([]\) \(891072000\) \(4.6982\) \(\Gamma_0(N)\)-optimal