Elliptic curve isogeny class with Cremona label 38720bm (LMFDB label 38720.dd)

• Label: 38720bm
• Number of curves: $4$
• Conductor: $38720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 38720bm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 38720bm do not have complex multiplication.

Modular form 38720.2.a.bm

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 38720bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38720.dd3	38720bm1	\([0, -1, 0, -645, -4123]\)	\(16384/5\)	\(9070392320\)	\([2]\)	\(23040\)	\(0.61557\)	\(\Gamma_0(N)\)-optimal
38720.dd4	38720bm2	\([0, -1, 0, 1775, -29775]\)	\(21296/25\)	\(-725631385600\)	\([2]\)	\(46080\)	\(0.96214\)
38720.dd1	38720bm3	\([0, -1, 0, -20005, 1095525]\)	\(488095744/125\)	\(226759808000\)	\([2]\)	\(69120\)	\(1.1649\)
38720.dd2	38720bm4	\([0, -1, 0, -17585, 1368017]\)	\(-20720464/15625\)	\(-453519616000000\)	\([2]\)	\(138240\)	\(1.5115\)