Elliptic curve isogeny class with Cremona label 17550bg (LMFDB label 17550.bp)

• Label: 17550bg
• Number of curves: $2$
• Conductor: $17550$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 17550bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17550bg do not have complex multiplication.

Modular form 17550.2.a.bg

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 17550bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17550.bp1	17550bg1	\([1, -1, 0, -102, 436]\)	\(-174828915/6656\)	\(-4492800\)	\([]\)	\(7128\)	\(0.046420\)	\(\Gamma_0(N)\)-optimal
17550.bp2	17550bg2	\([1, -1, 0, 498, 1196]\)	\(27726165/17576\)	\(-8648710200\)	\([]\)	\(21384\)	\(0.59573\)