Elliptic curve isogeny class with Cremona label 62400ej (LMFDB label 62400.dz)

• Label: 62400ej
• Number of curves: $4$
• Conductor: $62400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 62400ej have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 62400ej do not have complex multiplication.

Modular form 62400.2.a.ej

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 62400ej

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
62400.dz4	62400ej1	\([0, -1, 0, -461633, -199288863]\)	\(-2656166199049/2658140160\)	\(-10887742095360000000\)	\([2]\)	\(1474560\)	\(2.3486\)	\(\Gamma_0(N)\)-optimal
62400.dz3	62400ej2	\([0, -1, 0, -8653633, -9792120863]\)	\(17496824387403529/6580454400\)	\(26953541222400000000\)	\([2, 2]\)	\(2949120\)	\(2.6951\)
62400.dz2	62400ej3	\([0, -1, 0, -9933633, -6703480863]\)	\(26465989780414729/10571870144160\)	\(43302380110479360000000\)	\([2]\)	\(5898240\)	\(3.0417\)
62400.dz1	62400ej4	\([0, -1, 0, -138445633, -626953080863]\)	\(71647584155243142409/10140000\)	\(41533440000000000\)	\([2]\)	\(5898240\)	\(3.0417\)