Elliptic curve isogeny class with Cremona label 184800de (LMFDB label 184800.bl)

• Label: 184800de
• Number of curves: $4$
• Conductor: $184800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 184800de have rank \(1\).

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.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 184800.2.a.de

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 184800de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
184800.bl3	184800de1	\([0, -1, 0, -1358, -15288]\)	\(277167808/53361\)	\(53361000000\)	\([2, 2]\)	\(163840\)	\(0.77553\)	\(\Gamma_0(N)\)-optimal
184800.bl2	184800de2	\([0, -1, 0, -6608, 194712]\)	\(3989418056/307461\)	\(2459688000000\)	\([2]\)	\(327680\)	\(1.1221\)
184800.bl4	184800de3	\([0, -1, 0, 2767, -93663]\)	\(36594368/79233\)	\(-5070912000000\)	\([2]\)	\(327680\)	\(1.1221\)
184800.bl1	184800de4	\([0, -1, 0, -20608, -1131788]\)	\(120993582536/6237\)	\(49896000000\)	\([2]\)	\(327680\)	\(1.1221\)