Elliptic curve isogeny class with Cremona label 35550bw (LMFDB label 35550.bb)

• Label: 35550bw
• Number of curves: $4$
• Conductor: $35550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 35550bw have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35550bw do not have complex multiplication.

Modular form 35550.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 35550bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35550.bb4	35550bw1	\([1, -1, 1, 22495, 22497]\)	\(110522894399/63990000\)	\(-728886093750000\)	\([2]\)	\(196608\)	\(1.5413\)	\(\Gamma_0(N)\)-optimal
35550.bb3	35550bw2	\([1, -1, 1, -90005, 247497]\)	\(7078993977601/4094720100\)	\(46641421139062500\)	\([2, 2]\)	\(393216\)	\(1.8879\)
35550.bb2	35550bw3	\([1, -1, 1, -978755, -371250003]\)	\(9103276264946401/34006909590\)	\(387359954548593750\)	\([2]\)	\(786432\)	\(2.2345\)
35550.bb1	35550bw4	\([1, -1, 1, -1001255, 384794997]\)	\(9745628331520801/31549565610\)	\(359369270776406250\)	\([2]\)	\(786432\)	\(2.2345\)