Elliptic curve isogeny class with Cremona label 121680y (LMFDB label 121680.cr)

• Label: 121680y
• Number of curves: $4$
• Conductor: $121680$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 121680y have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 121680y do not have complex multiplication.

Modular form 121680.2.a.y

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 121680y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121680.cr4	121680y1	\([0, 0, 0, 5577, -74698]\)	\(21296/15\)	\(-13511976042240\)	\([2]\)	\(245760\)	\(1.2080\)	\(\Gamma_0(N)\)-optimal
121680.cr3	121680y2	\([0, 0, 0, -24843, -628342]\)	\(470596/225\)	\(810718562534400\)	\([2, 2]\)	\(491520\)	\(1.5546\)
121680.cr2	121680y3	\([0, 0, 0, -207363, 35912162]\)	\(136835858/1875\)	\(13511976042240000\)	\([2]\)	\(983040\)	\(1.9012\)
121680.cr1	121680y4	\([0, 0, 0, -329043, -72602062]\)	\(546718898/405\)	\(2918586825123840\)	\([2]\)	\(983040\)	\(1.9012\)