Elliptic curve isogeny class with LMFDB label 4896.k (Cremona label 4896d)

• Label: 4896.k
• Number of curves: $2$
• Conductor: $4896$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4896.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4896.k do not have complex multiplication.

Modular form 4896.2.a.k

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.

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

Isogeny graph

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

Elliptic curves in class 4896.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4896.k1	4896d1	\([0, 0, 0, -45, 108]\)	\(216000/17\)	\(793152\)	\([2]\)	\(512\)	\(-0.12417\)	\(\Gamma_0(N)\)-optimal
4896.k2	4896d2	\([0, 0, 0, 45, 486]\)	\(27000/289\)	\(-107868672\)	\([2]\)	\(1024\)	\(0.22240\)