Elliptic curve isogeny class with LMFDB label 177600.fe (Cremona label 177600fq)

• Label: 177600.fe
• Number of curves: $2$
• Conductor: $177600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 177600.fe have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.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 177600.fe do not have complex multiplication.

Modular form 177600.2.a.fe

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 177600.fe

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177600.fe1	177600fq2	\([0, 1, 0, -81633, 8884863]\)	\(14688124849/123210\)	\(504668160000000\)	\([2]\)	\(737280\)	\(1.6468\)
177600.fe2	177600fq1	\([0, 1, 0, -1633, 324863]\)	\(-117649/11100\)	\(-45465600000000\)	\([2]\)	\(368640\)	\(1.3002\)	\(\Gamma_0(N)\)-optimal