Elliptic curve isogeny class with LMFDB label 17850.bp (Cremona label 17850bs)

• Label: 17850.bp
• Number of curves: $4$
• Conductor: $17850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 17850.bp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17850.bp do not have complex multiplication.

Modular form 17850.2.a.bp

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 17850.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17850.bp1	17850bs3	\([1, 0, 0, -141005438, 644457063492]\)	\(19843180007106582309156121/1586964960000\)	\(24796327500000000\)	\([2]\)	\(1474560\)	\(3.0367\)
17850.bp2	17850bs2	\([1, 0, 0, -8813438, 10067655492]\)	\(4845512858070228485401/1370018429337600\)	\(21406537958400000000\)	\([2, 2]\)	\(737280\)	\(2.6902\)
17850.bp3	17850bs4	\([1, 0, 0, -7693438, 12720935492]\)	\(-3223035316613162194201/2609328690805052160\)	\(-40770760793828940000000\)	\([2]\)	\(1474560\)	\(3.0367\)
17850.bp4	17850bs1	\([1, 0, 0, -621438, 114375492]\)	\(1698623579042432281/620987846492160\)	\(9702935101440000000\)	\([2]\)	\(368640\)	\(2.3436\)	\(\Gamma_0(N)\)-optimal