Elliptic curve isogeny class with LMFDB label 4900.o (Cremona label 4900e)

• Label: 4900.o
• Number of curves: $1$
• Conductor: $4900$
• CM: no
• Rank: $1$

Rank

The elliptic curve 4900.o1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4900.o do not have complex multiplication.

Modular form 4900.2.a.o

Elliptic curves in class 4900.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4900.o1	4900e1	\([0, 1, 0, 22867, 318863]\)	\(8192/5\)	\(-807072140000000\)	\([]\)	\(16128\)	\(1.5496\)	\(\Gamma_0(N)\)-optimal