Elliptic curve isogeny class with Cremona label 196650cb (LMFDB label 196650.di)

• Label: 196650cb
• Number of curves: $2$
• Conductor: $196650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 196650cb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 196650cb do not have complex multiplication.

Modular form 196650.2.a.cb

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 196650cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
196650.di2	196650cb1	\([1, -1, 1, 4345, -89153]\)	\(29503629/27968\)	\(-8601471000000\)	\([2]\)	\(368640\)	\(1.1691\)	\(\Gamma_0(N)\)-optimal
196650.di1	196650cb2	\([1, -1, 1, -22655, -791153]\)	\(4181062131/1527752\)	\(469855353375000\)	\([2]\)	\(737280\)	\(1.5156\)