Elliptic curve isogeny class with Cremona label 1968g (LMFDB label 1968.g)

• Label: 1968g
• Number of curves: $2$
• Conductor: $1968$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1968g have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1968g do not have complex multiplication.

Modular form 1968.2.a.g

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 1968g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1968.g1	1968g1	\([0, -1, 0, -24, -144]\)	\(-389017/2214\)	\(-9068544\)	\([]\)	\(480\)	\(0.018942\)	\(\Gamma_0(N)\)-optimal
1968.g2	1968g2	\([0, -1, 0, 216, 3696]\)	\(270840023/1654104\)	\(-6775209984\)	\([]\)	\(1440\)	\(0.56825\)