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

• Label: 390390ck
• Number of curves: $4$
• Conductor: $390390$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 390390ck have rank \(0\).

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
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 390390.2.a.ck

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 390390ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
390390.ck4	390390ck1	\([1, 0, 1, -6841293, -7361982392]\)	\(-7336316844655213969/604492922880000\)	\(-2917771880593489920000\)	\([2]\)	\(35389440\)	\(2.8645\)	\(\Gamma_0(N)\)-optimal
390390.ck3	390390ck2	\([1, 0, 1, -111540173, -453421090744]\)	\(31794905164720991157649/192099600000000\)	\(927228078176400000000\)	\([2, 2]\)	\(70778880\)	\(3.2111\)
390390.ck2	390390ck3	\([1, 0, 1, -113622253, -435614309752]\)	\(33608860073906150870929/2466782226562500000\)	\(11906686652211914062500000\)	\([2]\)	\(141557760\)	\(3.5577\)
390390.ck1	390390ck4	\([1, 0, 1, -1784640173, -29018592010744]\)	\(130231365028993807856757649/4753980000\)	\(22946553449820000\)	\([2]\)	\(141557760\)	\(3.5577\)