Elliptic curve isogeny class with Cremona label 344760cy (LMFDB label 344760.cy)

• Label: 344760cy
• Number of curves: $4$
• Conductor: $344760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 344760cy have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 344760cy do not have complex multiplication.

Modular form 344760.2.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 344760cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
344760.cy4	344760cy1	\([0, 1, 0, -3419940, 73894536288]\)	\(-3579968623693264/1906997690433375\)	\(-2356406685481735257696000\)	\([2]\)	\(61931520\)	\(3.3557\)	\(\Gamma_0(N)\)-optimal
344760.cy3	344760cy2	\([0, 1, 0, -285720920, 1839517785600]\)	\(521902963282042184836/6241849278890625\)	\(30851291418616605456000000\)	\([2, 2]\)	\(123863040\)	\(3.7023\)
344760.cy1	344760cy3	\([0, 1, 0, -4558331600, 118454444641248]\)	\(1059623036730633329075378/154307373046875\)	\(1525375420393500000000000\)	\([2]\)	\(247726080\)	\(4.0488\)
344760.cy2	344760cy4	\([0, 1, 0, -529925920, -1771004298400]\)	\(1664865424893526702418/826424127435466125\)	\(8169454420219197053634816000\)	\([2]\)	\(247726080\)	\(4.0488\)