Elliptic curve isogeny class with Cremona label 147600cg (LMFDB label 147600.ek)

• Label: 147600cg
• Number of curves: $2$
• Conductor: $147600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 147600cg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 147600cg do not have complex multiplication.

Modular form 147600.2.a.cg

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 147600cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
147600.ek1	147600cg1	\([0, 0, 0, -5475, 513250]\)	\(-389017/2214\)	\(-103296384000000\)	\([]\)	\(414720\)	\(1.3730\)	\(\Gamma_0(N)\)-optimal
147600.ek2	147600cg2	\([0, 0, 0, 48525, -12716750]\)	\(270840023/1654104\)	\(-77173876224000000\)	\([]\)	\(1244160\)	\(1.9223\)