Elliptic curve isogeny class with Cremona label 28224dy (LMFDB label 28224.ba)

• Label: 28224dy
• Number of curves: $2$
• Conductor: $28224$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 28224dy have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28224dy do not have complex multiplication.

Modular form 28224.2.a.dy

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 28224dy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28224.ba1	28224dy1	\([0, 0, 0, -1176, 13720]\)	\(55296/7\)	\(22769316864\)	\([2]\)	\(24576\)	\(0.71661\)	\(\Gamma_0(N)\)-optimal
28224.ba2	28224dy2	\([0, 0, 0, 1764, 71344]\)	\(11664/49\)	\(-2550163488768\)	\([2]\)	\(49152\)	\(1.0632\)