Elliptic curve isogeny class with Cremona label 6336bb (LMFDB label 6336.by)

• Label: 6336bb
• Number of curves: $4$
• Conductor: $6336$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6336bb have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6336bb do not have complex multiplication.

Modular form 6336.2.a.bb

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 6336bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6336.by4	6336bb1	\([0, 0, 0, -46839, 3098068]\)	\(243578556889408/52089208083\)	\(2430274092320448\)	\([2]\)	\(30720\)	\(1.6665\)	\(\Gamma_0(N)\)-optimal
6336.by2	6336bb2	\([0, 0, 0, -705684, 228159520]\)	\(13015685560572352/864536409\)	\(2581491884691456\)	\([2, 2]\)	\(61440\)	\(2.0131\)
6336.by1	6336bb3	\([0, 0, 0, -11290764, 14602698160]\)	\(6663712298552914184/29403\)	\(702375100416\)	\([2]\)	\(122880\)	\(2.3597\)
6336.by3	6336bb4	\([0, 0, 0, -662124, 257553808]\)	\(-1343891598641864/421900912521\)	\(-10078314994984845312\)	\([2]\)	\(122880\)	\(2.3597\)