Elliptic curve isogeny class with LMFDB label 300352.bg (Cremona label 300352bg)

• Label: 300352.bg
• Number of curves: $3$
• Conductor: $300352$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 300352.bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 300352.bg do not have complex multiplication.

Modular form 300352.2.a.bg

Isogeny matrix

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 300352.bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
300352.bg1	300352bg3	\([0, -1, 0, -10616769, -13311330719]\)	\(-10730978619193/6656\)	\(-82087086374518784\)	\([]\)	\(8211456\)	\(2.5663\)
300352.bg2	300352bg2	\([0, -1, 0, -104449, -25860703]\)	\(-10218313/17576\)	\(-216761212457713664\)	\([]\)	\(2737152\)	\(2.0170\)
300352.bg3	300352bg1	\([0, -1, 0, 11071, 732001]\)	\(12167/26\)	\(-320652681150464\)	\([]\)	\(912384\)	\(1.4677\)	\(\Gamma_0(N)\)-optimal