Elliptic curve isogeny class with LMFDB label 55506.r (Cremona label 55506p)

• Label: 55506.r
• Number of curves: $1$
• Conductor: $55506$
• CM: no
• Rank: $1$

Rank

The elliptic curve 55506.r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(29\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 55506.r do not have complex multiplication.

Modular form 55506.2.a.r

Elliptic curves in class 55506.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55506.r1	55506p1	\([1, 0, 1, -236339, 44228528]\)	\(-2454365649169/1609674\)	\(-957471634407354\)	\([]\)	\(604800\)	\(1.8142\)	\(\Gamma_0(N)\)-optimal