Elliptic curve isogeny class with LMFDB label 284400.dj (Cremona label 284400dj)

• Label: 284400.dj
• Number of curves: $4$
• Conductor: $284400$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 284400.dj have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(79\)	\(1 - T\)

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
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 284400.dj do not have complex multiplication.

Modular form 284400.2.a.dj

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 LMFDB 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 LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 284400.dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
284400.dj1	284400dj3	\([0, 0, 0, -6084075, 5776020250]\)	\(533826202534561/15997500\)	\(746379360000000000\)	\([2]\)	\(5898240\)	\(2.5281\)
284400.dj2	284400dj2	\([0, 0, 0, -396075, 82332250]\)	\(147281603041/22467600\)	\(1048248345600000000\)	\([2, 2]\)	\(2949120\)	\(2.1816\)
284400.dj3	284400dj1	\([0, 0, 0, -108075, -12419750]\)	\(2992209121/303360\)	\(14153564160000000\)	\([2]\)	\(1474560\)	\(1.8350\)	\(\Gamma_0(N)\)-optimal
284400.dj4	284400dj4	\([0, 0, 0, 683925, 452772250]\)	\(758301032159/2337004860\)	\(-109035298748160000000\)	\([4]\)	\(5898240\)	\(2.5281\)