Elliptic curve isogeny class with Cremona label 224400hx (LMFDB label 224400.bp)

• Label: 224400hx
• Number of curves: $2$
• Conductor: $224400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 224400hx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 224400hx do not have complex multiplication.

Modular form 224400.2.a.hx

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 224400hx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
224400.bp2	224400hx1	\([0, -1, 0, -3608, -60288]\)	\(324730948/85833\)	\(1373328000000\)	\([2]\)	\(294912\)	\(1.0376\)	\(\Gamma_0(N)\)-optimal
224400.bp1	224400hx2	\([0, -1, 0, -20608, 1095712]\)	\(30248395634/1499553\)	\(47985696000000\)	\([2]\)	\(589824\)	\(1.3842\)