Elliptic curve isogeny class with Cremona label 113760u (LMFDB label 113760.bo)

• Label: 113760u
• Number of curves: $2$
• Conductor: $113760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 113760u have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(79\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 113760u do not have complex multiplication.

Modular form 113760.2.a.u

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 113760u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
113760.bo2	113760u1	\([0, 0, 0, -5097, -139084]\)	\(313877446336/2527605\)	\(117927938880\)	\([2]\)	\(172032\)	\(0.95168\)	\(\Gamma_0(N)\)-optimal
113760.bo1	113760u2	\([0, 0, 0, -8652, 79904]\)	\(23987543104/12957975\)	\(38692306022400\)	\([2]\)	\(344064\)	\(1.2983\)