Elliptic curve isogeny class with LMFDB label 552.a (Cremona label 552a)

• Label: 552.a
• Number of curves: $2$
• Conductor: $552$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 552.a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 552.a do not have complex multiplication.

Modular form 552.2.a.a

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 552.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
552.a1	552a2	\([0, -1, 0, -1144, -14516]\)	\(80919167474/14283\)	\(29251584\)	\([2]\)	\(192\)	\(0.43747\)
552.a2	552a1	\([0, -1, 0, -64, -260]\)	\(-28756228/16767\)	\(-17169408\)	\([2]\)	\(96\)	\(0.090899\)	\(\Gamma_0(N)\)-optimal