Elliptic curve isogeny class with Cremona label 296450hy (LMFDB label 296450.hy)

• Label: 296450hy
• Number of curves: $4$
• Conductor: $296450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 296450hy have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 296450hy do not have complex multiplication.

Modular form 296450.2.a.hy

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 296450hy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
296450.hy4	296450hy1	\([1, -1, 1, -546580, -5116242953]\)	\(-5545233/3469312\)	\(-11298160379864512000000\)	\([2]\)	\(17694720\)	\(2.9106\)	\(\Gamma_0(N)\)-optimal
296450.hy3	296450hy2	\([1, -1, 1, -47978580, -126542162953]\)	\(3750606459153/45914176\)	\(149524091277269401000000\)	\([2, 2]\)	\(35389440\)	\(3.2572\)
296450.hy2	296450hy3	\([1, -1, 1, -89481580, 125132029047]\)	\(24331017010833/12004097336\)	\(39092539649830380357875000\)	\([2]\)	\(70778880\)	\(3.6038\)
296450.hy1	296450hy4	\([1, -1, 1, -765387580, -8150044418953]\)	\(15226621995131793/2324168\)	\(7568884785729546125000\)	\([2]\)	\(70778880\)	\(3.6038\)