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 \((i,j)\)-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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 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	\([0, 1, 0, -355353112, -2591559610732]\)	\(-10298071306410575356297/60769798505543808\)	\(-29284376675855251322437632\)	\([2]\)	\(29030400\)	\(3.7271\)