Elliptic curve isogeny class with Cremona label 48672bm (LMFDB label 48672.be)

• Label: 48672bm
• Number of curves: $2$
• Conductor: $48672$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 48672bm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 48672bm do not have complex multiplication.

Modular form 48672.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 48672bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48672.be2	48672bm1	\([0, 0, 0, -27885, -1775176]\)	\(10648000/117\)	\(26348353282368\)	\([2]\)	\(86016\)	\(1.3899\)	\(\Gamma_0(N)\)-optimal
48672.be1	48672bm2	\([0, 0, 0, -50700, 1546688]\)	\(1000000/507\)	\(7307276643643392\)	\([2]\)	\(172032\)	\(1.7365\)