Elliptic curve isogeny class with Cremona label 63162bw (LMFDB label 63162.bx)

• Label: 63162bw
• Number of curves: $4$
• Conductor: $63162$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 63162bw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 63162bw do not have complex multiplication.

Modular form 63162.2.a.bw

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 63162bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63162.bx4	63162bw1	\([1, -1, 1, -4996355, 4295804483]\)	\(10680703423890625/11653595712\)	\(15050245585723748928\)	\([2]\)	\(2488320\)	\(2.5951\)	\(\Gamma_0(N)\)-optimal
63162.bx3	63162bw2	\([1, -1, 1, -6259595, 1956789299]\)	\(21002873311842625/10875667967208\)	\(14045576821128474360552\)	\([2]\)	\(4976640\)	\(2.9417\)
63162.bx2	63162bw3	\([1, -1, 1, -18521735, -26181463525]\)	\(544107922591866625/85504662747108\)	\(110426533138037529383652\)	\([2]\)	\(7464960\)	\(3.1445\)
63162.bx1	63162bw4	\([1, -1, 1, -284117945, -1843178255377]\)	\(1963975500122834382625/62995224591882\)	\(81356314760376700427658\)	\([2]\)	\(14929920\)	\(3.4910\)