Elliptic curve isogeny class with Cremona label 304920cy (LMFDB label 304920.cy)

• Label: 304920cy
• Number of curves: $4$
• Conductor: $304920$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 304920cy have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 304920cy do not have complex multiplication.

Modular form 304920.2.a.cy

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 304920cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
304920.cy3	304920cy1	\([0, 0, 0, -257367, 24338666]\)	\(5702413264/2525985\)	\(835130551724663040\)	\([2]\)	\(3932160\)	\(2.1345\)	\(\Gamma_0(N)\)-optimal
304920.cy2	304920cy2	\([0, 0, 0, -2021547, -1089564586]\)	\(690862540036/12006225\)	\(15877790736493593600\)	\([2, 2]\)	\(7864320\)	\(2.4811\)
304920.cy4	304920cy3	\([0, 0, 0, -61347, -3112098946]\)	\(-9653618/1581886845\)	\(-4183974278963134064640\)	\([2]\)	\(15728640\)	\(2.8277\)
304920.cy1	304920cy4	\([0, 0, 0, -32208627, -70356838354]\)	\(1397097631688978/433125\)	\(1145583747221760000\)	\([2]\)	\(15728640\)	\(2.8277\)