Elliptic curve isogeny class with Cremona label 154800cl (LMFDB label 154800.dj)

• Label: 154800cl
• Number of curves: $4$
• Conductor: $154800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 154800cl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 154800cl do not have complex multiplication.

Modular form 154800.2.a.cl

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 154800cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
154800.dj3	154800cl1	\([0, 0, 0, -88275, -10088750]\)	\(1630532233/1161\)	\(54167616000000\)	\([2]\)	\(491520\)	\(1.5709\)	\(\Gamma_0(N)\)-optimal
154800.dj2	154800cl2	\([0, 0, 0, -106275, -5678750]\)	\(2845178713/1347921\)	\(62888602176000000\)	\([2, 2]\)	\(983040\)	\(1.9174\)
154800.dj1	154800cl3	\([0, 0, 0, -880275, 313983250]\)	\(1616855892553/22851963\)	\(1066181185728000000\)	\([2]\)	\(1966080\)	\(2.2640\)
154800.dj4	154800cl4	\([0, 0, 0, 379725, -43100750]\)	\(129784785047/92307627\)	\(-4306704645312000000\)	\([2]\)	\(1966080\)	\(2.2640\)