Elliptic curve isogeny class with Cremona label 96432cy (LMFDB label 96432.ct)

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

Rank

The elliptic curves in class 96432cy 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 96432.2.a.cy

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 96432cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
96432.ct1	96432cy1	\([0, 1, 0, -355854872, -2583910179180]\)	\(10341755683137709164937/356992303104\)	\(172031129468446703616\)	\([2]\)	\(14515200\)	\(3.3805\)	\(\Gamma_0(N)\)-optimal
96432.ct2	96432cy2	\([0, 1, 0, -355353112, -2591559610732]\)	\(-10298071306410575356297/60769798505543808\)	\(-29284376675855251322437632\)	\([2]\)	\(29030400\)	\(3.7271\)