Elliptic curve isogeny class with Cremona label 57600cn (LMFDB label 57600.bk)

• Label: 57600cn
• Number of curves: $2$
• Conductor: $57600$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $1$

Rank

The elliptic curves in class 57600cn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

Each elliptic curve in class 57600cn has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 57600.2.a.cn

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 57600cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
57600.bk2	57600cn1	\([0, 0, 0, -750, 7000]\)	\(8000\)	\(5832000000\)	\([2]\)	\(27648\)	\(0.60348\)	\(\Gamma_0(N)\)-optimal	\(-8\)
57600.bk1	57600cn2	\([0, 0, 0, -3000, -56000]\)	\(8000\)	\(373248000000\)	\([2]\)	\(55296\)	\(0.95005\)		\(-8\)