Elliptic curve isogeny class with Cremona label 244800jn (LMFDB label 244800.jn)

• Label: 244800jn
• Number of curves: $4$
• Conductor: $244800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 244800jn have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 244800jn do not have complex multiplication.

Modular form 244800.2.a.jn

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 244800jn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
244800.jn3	244800jn1	\([0, 0, 0, -2065800, -1142827000]\)	\(83587439220736/6885\)	\(80306640000000\)	\([2]\)	\(2359296\)	\(2.1116\)	\(\Gamma_0(N)\)-optimal
244800.jn2	244800jn2	\([0, 0, 0, -2070300, -1137598000]\)	\(5258429611216/47403225\)	\(8846579462400000000\)	\([2, 2]\)	\(4718592\)	\(2.4582\)
244800.jn1	244800jn3	\([0, 0, 0, -3600300, 768782000]\)	\(6913728144004/3658971285\)	\(2731407428367360000000\)	\([2]\)	\(9437184\)	\(2.8048\)
244800.jn4	244800jn4	\([0, 0, 0, -612300, -2709322000]\)	\(-34008619684/4228250625\)	\(-3156372178560000000000\)	\([2]\)	\(9437184\)	\(2.8048\)