Elliptic curve isogeny class with Cremona label 47850bw (LMFDB label 47850.bx)

• Label: 47850bw
• Number of curves: $4$
• Conductor: $47850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 47850bw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(29\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 47850bw do not have complex multiplication.

Modular form 47850.2.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 47850bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47850.bx4	47850bw1	\([1, 1, 1, 962, 17531]\)	\(6300872423/11759616\)	\(-183744000000\)	\([2]\)	\(49152\)	\(0.84608\)	\(\Gamma_0(N)\)-optimal
47850.bx3	47850bw2	\([1, 1, 1, -7038, 177531]\)	\(2467489596697/527529024\)	\(8242641000000\)	\([2, 2]\)	\(98304\)	\(1.1926\)
47850.bx2	47850bw3	\([1, 1, 1, -36038, -2490469]\)	\(331273336732057/22285827432\)	\(348216053625000\)	\([2]\)	\(196608\)	\(1.5392\)
47850.bx1	47850bw4	\([1, 1, 1, -106038, 13245531]\)	\(8438952173768857/560166552\)	\(8752602375000\)	\([2]\)	\(196608\)	\(1.5392\)