Elliptic curve isogeny class with Cremona label 18240cy (LMFDB label 18240.co)

• Label: 18240cy
• Number of curves: $4$
• Conductor: $18240$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 18240cy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 18240cy do not have complex multiplication.

Modular form 18240.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 18240cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18240.co3	18240cy1	\([0, 1, 0, -1655745, -828126657]\)	\(-1914980734749238129/20440940544000\)	\(-5358469917966336000\)	\([2]\)	\(552960\)	\(2.4102\)	\(\Gamma_0(N)\)-optimal
18240.co2	18240cy2	\([0, 1, 0, -26559425, -52692530625]\)	\(7903870428425797297009/886464000000\)	\(232381218816000000\)	\([2]\)	\(1105920\)	\(2.7568\)
18240.co4	18240cy3	\([0, 1, 0, 5471295, -4306073025]\)	\(69096190760262356111/70568821500000000\)	\(-18499193143296000000000\)	\([2]\)	\(1658880\)	\(2.9595\)
18240.co1	18240cy4	\([0, 1, 0, -29646785, -39684026817]\)	\(10993009831928446009969/3767761230468750000\)	\(987696000000000000000000\)	\([2]\)	\(3317760\)	\(3.3061\)