Elliptic curve isogeny class with Cremona label 171600bw (LMFDB label 171600.fs)

• Label: 171600bw
• Number of curves: $2$
• Conductor: $171600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 171600bw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 171600bw do not have complex multiplication.

Modular form 171600.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 171600bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171600.fs2	171600bw1	\([0, 1, 0, -267008, -71400012]\)	\(-32894113444921/15289560000\)	\(-978531840000000000\)	\([2]\)	\(2211840\)	\(2.1583\)	\(\Gamma_0(N)\)-optimal
171600.fs1	171600bw2	\([0, 1, 0, -4667008, -3881800012]\)	\(175654575624148921/21954418200\)	\(1405082764800000000\)	\([2]\)	\(4423680\)	\(2.5049\)