Elliptic curve isogeny class with Cremona label 183456cy (LMFDB label 183456.cd)

• Label: 183456cy
• Number of curves: $2$
• Conductor: $183456$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 183456cy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 183456cy do not have complex multiplication.

Modular form 183456.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 183456cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183456.cd2	183456cy1	\([0, 0, 0, -8085, 277144]\)	\(10648000/117\)	\(642216714048\)	\([2]\)	\(184320\)	\(1.0804\)	\(\Gamma_0(N)\)-optimal
183456.cd1	183456cy2	\([0, 0, 0, -14700, -241472]\)	\(1000000/507\)	\(178108102029312\)	\([2]\)	\(368640\)	\(1.4269\)