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

• Label: 1968l
• Number of curves: $2$
• Conductor: $1968$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1968l have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 1968.2.a.l

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.

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

Isogeny graph

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

Elliptic curves in class 1968l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1968.h1	1968l1	\([0, 1, 0, -1064, -13644]\)	\(32553430057/212544\)	\(870580224\)	\([2]\)	\(1152\)	\(0.55128\)	\(\Gamma_0(N)\)-optimal
1968.h2	1968l2	\([0, 1, 0, -424, -29260]\)	\(-2062933417/88232328\)	\(-361399615488\)	\([2]\)	\(2304\)	\(0.89786\)