Elliptic curve isogeny class with LMFDB label 121296.cs (Cremona label 121296cm)

• Label: 121296.cs
• Number of curves: $4$
• Conductor: $121296$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 121296.cs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121296.cs do not have complex multiplication.

Modular form 121296.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 121296.cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121296.cs1	121296cm4	\([0, 1, 0, -660028, -206611384]\)	\(2640279346000/3087\)	\(37179042469632\)	\([2]\)	\(995328\)	\(1.8870\)
121296.cs2	121296cm3	\([0, 1, 0, -40913, -3294018]\)	\(-10061824000/352947\)	\(-265675240980912\)	\([2]\)	\(497664\)	\(1.5405\)
121296.cs3	121296cm2	\([0, 1, 0, -10228, -130936]\)	\(9826000/5103\)	\(61459233470208\)	\([2]\)	\(331776\)	\(1.3377\)
121296.cs4	121296cm1	\([0, 1, 0, 2407, -14694]\)	\(2048000/1323\)	\(-995867209008\)	\([2]\)	\(165888\)	\(0.99115\)	\(\Gamma_0(N)\)-optimal