Elliptic curve isogeny class with Cremona label 117600y (LMFDB label 117600.du)

• Label: 117600y
• Number of curves: $4$
• Conductor: $117600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 117600y have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 117600y do not have complex multiplication.

Modular form 117600.2.a.y

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 117600y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117600.du3	117600y1	\([0, -1, 0, -277258, -54984488]\)	\(20034997696/455625\)	\(53603825625000000\)	\([2, 2]\)	\(1327104\)	\(1.9967\)	\(\Gamma_0(N)\)-optimal
117600.du4	117600y2	\([0, -1, 0, 28992, -170134488]\)	\(2863288/13286025\)	\(-12504700441800000000\)	\([2]\)	\(2654208\)	\(2.3433\)
117600.du2	117600y3	\([0, -1, 0, -608008, 101791012]\)	\(26410345352/10546875\)	\(9926634375000000000\)	\([2]\)	\(2654208\)	\(2.3433\)
117600.du1	117600y4	\([0, -1, 0, -4411633, -3565068863]\)	\(1261112198464/675\)	\(5082436800000000\)	\([2]\)	\(2654208\)	\(2.3433\)