Elliptic curve isogeny class with LMFDB label 121680.o (Cremona label 121680dx)

• Label: 121680.o
• Number of curves: $1$
• Conductor: $121680$
• CM: no
• Rank: $1$

Rank

The elliptic curve 121680.o1 has rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 121680.2.a.o

Elliptic curves in class 121680.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121680.o1	121680dx1	\([0, 0, 0, -19773, 771147]\)	\(89856/25\)	\(237867078243600\)	\([]\)	\(419328\)	\(1.4658\)	\(\Gamma_0(N)\)-optimal