Elliptic curve isogeny class with Cremona label 196800gy (LMFDB label 196800.gl)

• Label: 196800gy
• Number of curves: $2$
• Conductor: $196800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 196800gy have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 196800gy do not have complex multiplication.

Modular form 196800.2.a.gy

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 196800gy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
196800.gl1	196800gy1	\([0, 1, 0, -726234433, -7533162080737]\)	\(10341755683137709164937/356992303104\)	\(1462240473513984000000\)	\([2]\)	\(41287680\)	\(3.5588\)	\(\Gamma_0(N)\)-optimal
196800.gl2	196800gy2	\([0, 1, 0, -725210433, -7555463776737]\)	\(-10298071306410575356297/60769798505543808\)	\(-248913094678707437568000000\)	\([2]\)	\(82575360\)	\(3.9054\)