Elliptic curve isogeny class with LMFDB label 113288.o (Cremona label 113288r)

• Label: 113288.o
• Number of curves: $1$
• Conductor: $113288$
• CM: no
• Rank: $0$

Rank

The elliptic curve 113288.o1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 113288.o do not have complex multiplication.

Modular form 113288.2.a.o

Elliptic curves in class 113288.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
113288.o1	113288r1	\([0, 0, 0, -1515227, -718840682]\)	\(-3241463778/4913\)	\(-583125998529120256\)	\([]\)	\(1575936\)	\(2.3091\)	\(\Gamma_0(N)\)-optimal