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

• Label: 1968i
• Number of curves: $4$
• Conductor: $1968$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1968i 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 1968.2.a.i

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 1968i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1968.b3	1968i1	\([0, -1, 0, -144, -576]\)	\(81182737/5904\)	\(24182784\)	\([2]\)	\(576\)	\(0.16314\)	\(\Gamma_0(N)\)-optimal
1968.b2	1968i2	\([0, -1, 0, -464, 3264]\)	\(2703045457/544644\)	\(2230861824\)	\([2, 2]\)	\(1152\)	\(0.50972\)
1968.b1	1968i3	\([0, -1, 0, -7024, 228928]\)	\(9357915116017/538002\)	\(2203656192\)	\([2]\)	\(2304\)	\(0.85629\)
1968.b4	1968i4	\([0, -1, 0, 976, 18240]\)	\(25076571983/50863698\)	\(-208337707008\)	\([4]\)	\(2304\)	\(0.85629\)