Elliptic curve isogeny class with Cremona label 177600cd (LMFDB label 177600.jd)

• Label: 177600cd
• Number of curves: $4$
• Conductor: $177600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 177600cd have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177600cd do not have complex multiplication.

Modular form 177600.2.a.cd

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 177600cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177600.jd3	177600cd1	\([0, 1, 0, -33508, -2371762]\)	\(4160851280704/624375\)	\(624375000000\)	\([2]\)	\(442368\)	\(1.2765\)	\(\Gamma_0(N)\)-optimal
177600.jd2	177600cd2	\([0, 1, 0, -36633, -1906137]\)	\(84951891136/24950025\)	\(1596801600000000\)	\([2, 2]\)	\(884736\)	\(1.6231\)
177600.jd1	177600cd3	\([0, 1, 0, -221633, 38608863]\)	\(2351575819592/98316585\)	\(50338091520000000\)	\([4]\)	\(1769472\)	\(1.9697\)
177600.jd4	177600cd4	\([0, 1, 0, 98367, -12571137]\)	\(205587930808/253011735\)	\(-129542008320000000\)	\([2]\)	\(1769472\)	\(1.9697\)