Elliptic curve isogeny class with LMFDB label 96432.bz (Cremona label 96432dd)

• Label: 96432.bz
• Number of curves: $2$
• Conductor: $96432$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 96432.bz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 96432.bz do not have complex multiplication.

Modular form 96432.2.a.bz

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 96432.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
96432.bz1	96432dd1	\([0, 1, 0, -1192, 51764]\)	\(-389017/2214\)	\(-1066905133056\)	\([]\)	\(172800\)	\(0.99190\)	\(\Gamma_0(N)\)-optimal
96432.bz2	96432dd2	\([0, 1, 0, 10568, -1288876]\)	\(270840023/1654104\)	\(-797096679407616\)	\([]\)	\(518400\)	\(1.5412\)