Elliptic curve isogeny class with LMFDB label 8256.f (Cremona label 8256j)

• Label: 8256.f
• Number of curves: $4$
• Conductor: $8256$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 8256.f have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 8256.f do not have complex multiplication.

Modular form 8256.2.a.f

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 8256.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8256.f1	8256j3	\([0, -1, 0, -15649, 749473]\)	\(1616855892553/22851963\)	\(5990504988672\)	\([2]\)	\(15360\)	\(1.2565\)
8256.f2	8256j2	\([0, -1, 0, -1889, -12831]\)	\(2845178713/1347921\)	\(353349402624\)	\([2, 2]\)	\(7680\)	\(0.90997\)
8256.f3	8256j1	\([0, -1, 0, -1569, -23391]\)	\(1630532233/1161\)	\(304349184\)	\([2]\)	\(3840\)	\(0.56340\)	\(\Gamma_0(N)\)-optimal
8256.f4	8256j4	\([0, -1, 0, 6751, -104415]\)	\(129784785047/92307627\)	\(-24197890572288\)	\([2]\)	\(15360\)	\(1.2565\)