Elliptic curve isogeny class with LMFDB label 118976.bw (Cremona label 118976t)

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

Rank

The elliptic curves in class 118976.bw 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 118976.2.a.bw

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 118976.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
118976.bw1	118976t1	\([0, 0, 0, -2080, -36504]\)	\(442368000/121\)	\(272217088\)	\([2]\)	\(57600\)	\(0.60114\)	\(\Gamma_0(N)\)-optimal
118976.bw2	118976t2	\([0, 0, 0, -1820, -45968]\)	\(-18522000/14641\)	\(-527012282368\)	\([2]\)	\(115200\)	\(0.94772\)