Elliptic curve isogeny class with Cremona label 138384r (LMFDB label 138384.cm)

• Label: 138384r
• Number of curves: $4$
• Conductor: $138384$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 138384r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 138384r do not have complex multiplication.

Modular form 138384.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 138384r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
138384.cm4	138384r1	\([0, 0, 0, -95139, -56304990]\)	\(-35937/496\)	\(-1314435608537923584\)	\([2]\)	\(1474560\)	\(2.1582\)	\(\Gamma_0(N)\)-optimal
138384.cm3	138384r2	\([0, 0, 0, -2862819, -1858064670]\)	\(979146657/3844\)	\(10186875966168907776\)	\([2, 2]\)	\(2949120\)	\(2.5048\)
138384.cm2	138384r3	\([0, 0, 0, -4246659, 123870978]\)	\(3196010817/1847042\)	\(4894793901744160186368\)	\([2]\)	\(5898240\)	\(2.8514\)
138384.cm1	138384r4	\([0, 0, 0, -45761859, -119152619838]\)	\(3999236143617/62\)	\(164304451067240448\)	\([2]\)	\(5898240\)	\(2.8514\)