Elliptic curve isogeny class with LMFDB label 13680.bh (Cremona label 13680bo)

• Label: 13680.bh
• Number of curves: $4$
• Conductor: $13680$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13680.bh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 13680.bh do not have complex multiplication.

Modular form 13680.2.a.bh

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 13680.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13680.bh1	13680bo4	\([0, 0, 0, -66705267, 133900237874]\)	\(10993009831928446009969/3767761230468750000\)	\(11250474750000000000000000\)	\([2]\)	\(3317760\)	\(3.5088\)
13680.bh2	13680bo2	\([0, 0, 0, -59758707, 177807411506]\)	\(7903870428425797297009/886464000000\)	\(2646967320576000000\)	\([2]\)	\(1105920\)	\(2.9595\)
13680.bh3	13680bo1	\([0, 0, 0, -3725427, 2793064754]\)	\(-1914980734749238129/20440940544000\)	\(-61036321409335296000\)	\([2]\)	\(552960\)	\(2.6129\)	\(\Gamma_0(N)\)-optimal
13680.bh4	13680bo3	\([0, 0, 0, 12310413, 14539151666]\)	\(69096190760262356111/70568821500000000\)	\(-210717371897856000000000\)	\([2]\)	\(1658880\)	\(3.1622\)