Elliptic curve isogeny class with Cremona label 196800fo (LMFDB label 196800.fc)

• Label: 196800fo
• Number of curves: $4$
• Conductor: $196800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 196800fo have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 196800.2.a.fo

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 196800fo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
196800.fc3	196800fo1	\([0, -1, 0, -14433, -619263]\)	\(81182737/5904\)	\(24182784000000\)	\([2]\)	\(589824\)	\(1.3144\)	\(\Gamma_0(N)\)-optimal
196800.fc2	196800fo2	\([0, -1, 0, -46433, 3124737]\)	\(2703045457/544644\)	\(2230861824000000\)	\([2, 2]\)	\(1179648\)	\(1.6610\)
196800.fc1	196800fo3	\([0, -1, 0, -702433, 226820737]\)	\(9357915116017/538002\)	\(2203656192000000\)	\([2]\)	\(2359296\)	\(2.0076\)
196800.fc4	196800fo4	\([0, -1, 0, 97567, 18532737]\)	\(25076571983/50863698\)	\(-208337707008000000\)	\([2]\)	\(2359296\)	\(2.0076\)