Elliptic curve isogeny class with LMFDB label 256.d (Cremona label 256d)

• Label: 256.d
• Number of curves: $2$
• Conductor: $256$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $0$

Rank

The elliptic curves in class 256.d have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 256.d has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 256.2.a.d

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 256.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
256.d1	256d2	\([0, -1, 0, -13, 21]\)	\(8000\)	\(32768\)	\([2]\)	\(16\)	\(-0.40397\)		\(-8\)
256.d2	256d1	\([0, -1, 0, -3, -1]\)	\(8000\)	\(512\)	\([2]\)	\(8\)	\(-0.75055\)	\(\Gamma_0(N)\)-optimal	\(-8\)