Elliptic curve isogeny class with Cremona label 117360bx (LMFDB label 117360.bo)

• Label: 117360bx
• Number of curves: $4$
• Conductor: $117360$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 117360bx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(163\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 117360bx do not have complex multiplication.

Modular form 117360.2.a.bx

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 117360bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117360.bo3	117360bx1	\([0, 0, 0, -120027, -16000054]\)	\(64043209720729/24755625\)	\(73919900160000\)	\([2]\)	\(491520\)	\(1.6266\)	\(\Gamma_0(N)\)-optimal
117360.bo2	117360bx2	\([0, 0, 0, -138027, -10884454]\)	\(97393143178729/39221822025\)	\(117115733017497600\)	\([2, 2]\)	\(983040\)	\(1.9731\)
117360.bo4	117360bx3	\([0, 0, 0, 448773, -79070614]\)	\(3347467708032071/2841729286815\)	\(-8485358182761000960\)	\([2]\)	\(1966080\)	\(2.3197\)
117360.bo1	117360bx4	\([0, 0, 0, -1012827, 384700106]\)	\(38480618749557529/857682789615\)	\(2561027086865756160\)	\([4]\)	\(1966080\)	\(2.3197\)