Elliptic curve isogeny class with LMFDB label 390390.dj (Cremona label 390390dj)

• Label: 390390.dj
• Number of curves: $4$
• Conductor: $390390$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 390390.dj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 390390.dj do not have complex multiplication.

Modular form 390390.2.a.dj

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 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.

Elliptic curves in class 390390.dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
390390.dj1	390390dj3	\([1, 1, 1, -2059015, 1131285605]\)	\(200005594092187129/1027287538200\)	\(4958520734971603800\)	\([2]\)	\(11796480\)	\(2.4333\)
390390.dj2	390390dj2	\([1, 1, 1, -200015, -4191595]\)	\(183337554283129/104587560000\)	\(504824175896040000\)	\([2, 2]\)	\(5898240\)	\(2.0867\)
390390.dj3	390390dj1	\([1, 1, 1, -145935, -21475563]\)	\(71210194441849/165580800\)	\(799226895667200\)	\([2]\)	\(2949120\)	\(1.7401\)	\(\Gamma_0(N)\)-optimal
390390.dj4	390390dj4	\([1, 1, 1, 793705, -32413243]\)	\(11456208593737991/6725709375000\)	\(-32463714542634375000\)	\([2]\)	\(11796480\)	\(2.4333\)