Elliptic curve isogeny class with Cremona label 188496cs (LMFDB label 188496.dx)

• Label: 188496cs
• Number of curves: $2$
• Conductor: $188496$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 188496cs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 188496cs do not have complex multiplication.

Modular form 188496.2.a.cs

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 188496cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
188496.dx2	188496cs1	\([0, 0, 0, -551043, 38082690]\)	\(229524442504083/125055451136\)	\(10082166557531701248\)	\([2]\)	\(4644864\)	\(2.3373\)	\(\Gamma_0(N)\)-optimal
188496.dx1	188496cs2	\([0, 0, 0, -5251203, -4600975230]\)	\(198631853028508563/1517849044096\)	\(122371369922320662528\)	\([2]\)	\(9289728\)	\(2.6839\)