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

• Label: 576.c
• Number of curves: $4$
• Conductor: $576$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Rank

The elliptic curves in class 576.c have rank \(1\).

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.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 576.c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 576.2.a.c

Isogeny matrix

The \(i,j\) 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 576.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
576.c1	576h3	\([0, 0, 0, -396, -3024]\)	\(287496\)	\(23887872\)	\([2]\)	\(128\)	\(0.27849\)		\(-16\)
576.c2	576h4	\([0, 0, 0, -396, 3024]\)	\(287496\)	\(23887872\)	\([2]\)	\(128\)	\(0.27849\)		\(-16\)
576.c3	576h2	\([0, 0, 0, -36, 0]\)	\(1728\)	\(2985984\)	\([2, 2]\)	\(64\)	\(-0.068080\)		\(-4\)
576.c4	576h1	\([0, 0, 0, 9, 0]\)	\(1728\)	\(-46656\)	\([2]\)	\(32\)	\(-0.41465\)	\(\Gamma_0(N)\)-optimal	\(-4\)