Elliptic curve isogeny class with Cremona label 121680ey (LMFDB label 121680.dr)

• Label: 121680ey
• Number of curves: $2$
• Conductor: $121680$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 121680ey have rank \(2\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 121680.2.a.ey

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 121680ey

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121680.dr1	121680ey1	\([0, 0, 0, -122187, 16479866]\)	\(-2365581049/6750\)	\(-575658150912000\)	\([]\)	\(580608\)	\(1.7038\)	\(\Gamma_0(N)\)-optimal
121680.dr2	121680ey2	\([0, 0, 0, 242853, 84450314]\)	\(18573478391/46875000\)	\(-3997626048000000000\)	\([]\)	\(1741824\)	\(2.2532\)