Elliptic curve isogeny class with Cremona label 73920ik (LMFDB label 73920.im)

• Label: 73920ik
• Number of curves: $4$
• Conductor: $73920$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 73920ik have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 73920ik do not have complex multiplication.

Modular form 73920.2.a.ik

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 73920ik

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
73920.im4	73920ik1	\([0, 1, 0, -2590785, 1714677183]\)	\(-7336316844655213969/604492922880000\)	\(-158464192775454720000\)	\([2]\)	\(2949120\)	\(2.6218\)	\(\Gamma_0(N)\)-optimal
73920.im3	73920ik2	\([0, 1, 0, -42240065, 105651299775]\)	\(31794905164720991157649/192099600000000\)	\(50357757542400000000\)	\([2, 2]\)	\(5898240\)	\(2.9683\)
73920.im2	73920ik3	\([0, 1, 0, -43028545, 101501214143]\)	\(33608860073906150870929/2466782226562500000\)	\(646652160000000000000000\)	\([2]\)	\(11796480\)	\(3.3149\)
73920.im1	73920ik4	\([0, 1, 0, -675840065, 6762379619775]\)	\(130231365028993807856757649/4753980000\)	\(1246227333120000\)	\([2]\)	\(11796480\)	\(3.3149\)