Elliptic curve isogeny class with LMFDB label 212160.fs (Cremona label 212160by)

• Label: 212160.fs
• Number of curves: $2$
• Conductor: $212160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 212160.fs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(13\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 212160.fs do not have complex multiplication.

Modular form 212160.2.a.fs

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 212160.fs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212160.fs1	212160by2	\([0, 1, 0, -98961, 11509839]\)	\(6541847063933776/272710546875\)	\(4468089600000000\)	\([2]\)	\(1474560\)	\(1.7680\)
212160.fs2	212160by1	\([0, 1, 0, -16341, -569205]\)	\(471287826743296/138654433125\)	\(141982139520000\)	\([2]\)	\(737280\)	\(1.4214\)	\(\Gamma_0(N)\)-optimal