Elliptic curve isogeny class with LMFDB label 13248.bk (Cremona label 13248r)

• Label: 13248.bk
• Number of curves: $4$
• Conductor: $13248$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13248.bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13248.bk do not have complex multiplication.

Modular form 13248.2.a.bk

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 13248.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13248.bk1	13248r3	\([0, 0, 0, -142284, -20654480]\)	\(1666957239793/301806\)	\(57676024774656\)	\([2]\)	\(49152\)	\(1.6440\)
13248.bk2	13248r4	\([0, 0, 0, -61644, 5698672]\)	\(135559106353/5037138\)	\(962612062322688\)	\([2]\)	\(49152\)	\(1.6440\)
13248.bk3	13248r2	\([0, 0, 0, -9804, -252560]\)	\(545338513/171396\)	\(32754285674496\)	\([2, 2]\)	\(24576\)	\(1.2975\)
13248.bk4	13248r1	\([0, 0, 0, 1716, -26768]\)	\(2924207/3312\)	\(-632933056512\)	\([2]\)	\(12288\)	\(0.95089\)	\(\Gamma_0(N)\)-optimal