Elliptic curve isogeny class with LMFDB label 184800.cw (Cremona label 184800cn)

• Label: 184800.cw
• Number of curves: $4$
• Conductor: $184800$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 184800.cw have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 184800.cw do not have complex multiplication.

Modular form 184800.2.a.cw

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 184800.cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
184800.cw1	184800cn2	\([0, -1, 0, -1293608, 566738712]\)	\(29925549856274696/4851\)	\(38808000000\)	\([2]\)	\(1310720\)	\(1.8757\)
184800.cw2	184800cn4	\([0, -1, 0, -93233, 5990337]\)	\(1400416996672/570715299\)	\(36525779136000000\)	\([2]\)	\(1310720\)	\(1.8757\)
184800.cw3	184800cn1	\([0, -1, 0, -80858, 8873712]\)	\(58465284603328/23532201\)	\(23532201000000\)	\([2, 2]\)	\(655360\)	\(1.5292\)	\(\Gamma_0(N)\)-optimal
184800.cw4	184800cn3	\([0, -1, 0, -68608, 11642212]\)	\(-4464412682696/4706920449\)	\(-37655363592000000\)	\([2]\)	\(1310720\)	\(1.8757\)