Elliptic curve isogeny class with LMFDB label 576.g (Cremona label 576c)

• Label: 576.g
• Number of curves: $4$
• Conductor: $576$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 576.g have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 576.g do not have complex multiplication.

Modular form 576.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 576.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
576.g1	576c3	\([0, 0, 0, -1164, -15280]\)	\(7301384/3\)	\(71663616\)	\([2]\)	\(256\)	\(0.46966\)
576.g2	576c2	\([0, 0, 0, -84, -160]\)	\(21952/9\)	\(26873856\)	\([2, 2]\)	\(128\)	\(0.12309\)
576.g3	576c1	\([0, 0, 0, -39, 92]\)	\(140608/3\)	\(139968\)	\([2]\)	\(64\)	\(-0.22349\)	\(\Gamma_0(N)\)-optimal
576.g4	576c4	\([0, 0, 0, 276, -1168]\)	\(97336/81\)	\(-1934917632\)	\([2]\)	\(256\)	\(0.46966\)