Elliptic curve isogeny class with LMFDB label 19152.bj (Cremona label 19152bp)

• Label: 19152.bj
• Number of curves: $4$
• Conductor: $19152$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 19152.bj have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(19\)	\(1 - T\)

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
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19152.bj do not have complex multiplication.

Modular form 19152.2.a.bj

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 19152.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19152.bj1	19152bp3	\([0, 0, 0, -2613819, 1626526442]\)	\(661397832743623417/443352042\)	\(1323842103779328\)	\([4]\)	\(245760\)	\(2.2178\)
19152.bj2	19152bp2	\([0, 0, 0, -164379, 25082570]\)	\(164503536215257/4178071044\)	\(12475653288247296\)	\([2, 2]\)	\(122880\)	\(1.8712\)
19152.bj3	19152bp1	\([0, 0, 0, -23259, -798838]\)	\(466025146777/177366672\)	\(529614044725248\)	\([2]\)	\(61440\)	\(1.5246\)	\(\Gamma_0(N)\)-optimal
19152.bj4	19152bp4	\([0, 0, 0, 27141, 80048810]\)	\(740480746823/927484650666\)	\(-2769454327134265344\)	\([2]\)	\(245760\)	\(2.2178\)