Elliptic curve isogeny class with Cremona label 118976bg (LMFDB label 118976.bh)

• Label: 118976bg
• Number of curves: $2$
• Conductor: $118976$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 118976bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 118976bg do not have complex multiplication.

Modular form 118976.2.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 118976bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
118976.bh2	118976bg1	\([0, -1, 0, 61291, -2678963]\)	\(321978368/224939\)	\(-17788724668841984\)	\([]\)	\(645120\)	\(1.8066\)	\(\Gamma_0(N)\)-optimal
118976.bh1	118976bg2	\([0, -1, 0, -1128469, -471444403]\)	\(-2009615368192/53094899\)	\(-4198874093114015744\)	\([]\)	\(1935360\)	\(2.3559\)