Elliptic curve isogeny class with Cremona label 13872m (LMFDB label 13872.y)

• Label: 13872m
• Number of curves: $4$
• Conductor: $13872$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13872m have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13872m do not have complex multiplication.

Modular form 13872.2.a.m

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 13872m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13872.y3	13872m1	\([0, 1, 0, -15124, -719428]\)	\(61918288/153\)	\(945420302592\)	\([2]\)	\(36864\)	\(1.1758\)	\(\Gamma_0(N)\)-optimal
13872.y2	13872m2	\([0, 1, 0, -20904, -125244]\)	\(40873252/23409\)	\(578597225186304\)	\([2, 2]\)	\(73728\)	\(1.5223\)
13872.y1	13872m3	\([0, 1, 0, -217424, 38785716]\)	\(22994537186/111537\)	\(5513691204716544\)	\([4]\)	\(147456\)	\(1.8689\)
13872.y4	13872m4	\([0, 1, 0, 83136, -915948]\)	\(1285471294/751689\)	\(-37158799573075968\)	\([2]\)	\(147456\)	\(1.8689\)